Graphing is a very useful tool to solve a system of equations but the only major disadvantage is that it is very time-consuming. So, we can solve the system of equations quickly by isolation one variable in one equation and then we get the answer by substituting the resulting expression for the variable in the other equation.
Step-by-step explanation :
Step 1:
Consider the system of equations:
5x + y =13
3x=15 - 3y
Step 2 :
y is the easiest variable to isolate in the first equation, because it has no coefficient:
y = 13 - 5x
Step 3 :
In the second equation, substituting for y :
3x = 15 - 3(13 - 5x)
Step 4 :
Solve the equation:
3x = 15 - 39 + 15x
3x = 15x - 24
-12x = - 24
x = 2
substituting this x-value into the "isolated equation" to find y:
y = 13 - 5x = 13 - 5(2) = 13 - 10 = 3
The solution to the system is (2, 3). This point is used to check for solutions in both equations.
Interpreting the solution of a system of equations involves determining the type of solution (unique, infinitely many, or no solution) and understanding how it relates to the problem being solved. It allows us to find the specific values for the variables that satisfy all the equations and provides insights into the relationships between the variables.
Interpreting the solution of a system of equations is a crucial step in solving a problem. It allows us to understand the relationship between the variables and determine the values that satisfy all the equations in the system. Here's how you can interpret the solution:
1. Determine the type of solution: A system of equations can have three types of solutions: a unique solution, infinitely many solutions, or no solution. To determine the type of solution, solve the system of equations using methods such as substitution, elimination, or matrices.
2. Unique solution: If the system of equations has a unique solution, it means that there is only one set of values for the variables that satisfies all the equations. This solution represents the point where all the equations intersect. In practical terms, this means that there is a specific answer to the problem being solved.
3. Infinitely many solutions: If the system of equations has infinitely many solutions, it means that there are multiple sets of values for the variables that satisfy all the equations. This usually occurs when the equations represent the same line or planes that overlap. In practical terms, this may indicate that there are multiple valid solutions to the problem.
4. No solution: If the system of equations has no solution, it means that there are no values for the variables that satisfy all the equations simultaneously. This usually occurs when the equations represent parallel lines or planes that do not intersect. In practical terms, this may indicate that the problem being solved is not feasible or does not have a valid solution.
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Find the volume of the prism.
50 yd3
250 yd3
200 yd3
20 yd3
Answer:
[tex]V=200\ yd^3[/tex]
Step-by-step explanation:
we know that
The volume of the prism is equal to
[tex]V=LWH[/tex]
where
L is the length
W is the width
H is the height
we have
[tex]L=10\ yd\\W=5\ yd\\H=4\ yd[/tex]
substitute
[tex]V=(10)(5)(4)=200\ yd^3[/tex]
Answer:
C.) 200 yd3
Step-by-step evaluation:
Step 1.) 4 x 5 = 20
Step 2.) 20 x 10 = 200
Step 3. (Final answer).) C.) 200 yd3
Explanation:
4 times 5 will equal 20 because, 4 + 4 + 4 + 4 + 4, or 5 + 5 + 5 + 5, equals 20.
20 times 10 will equal, the answer, 200 hundred because 20 + 20 + 20 + 20 + 20 + 20 + 20 + 20 + 20 + 20 = 200, and that's our answer.
Final answer:
C.) 200 yd3
From 1980-1990, the population of a country was increased by 20%. From 1990-2000, the population of the country was increased by 20%. From 2000-2010, the population of the country was increased by 20%. Population (in percentage) of the country from 1980-2010 was increase by
please I need a good step by step explanation I try to resolved it but I can't do it
Answer:
The % of the increase in population from 1980 to 2000 will be 72.8%
Step-by-step explanation:
Let the population in the year of 1980 was x.
If the population from 1980 to 1990 has increased by 20%, then the population in the year 1990 will be [tex]x(1 + \frac{20}{100}) = 1.2x[/tex].
Now, from 1990 to 2000, the population has again increased by 20%.
So, the population in the year 2000 will be [tex]1.2x(1 + \frac{20}{100}) = 1.44x[/tex].
Again, from 2000 to 2010, the population has increased by 20%.
Therefore, the population in the year 2010 will be [tex]1.44x(1 + \frac{20}{100}) = 1.728x[/tex].
Now, the population increased from x to 1.728x between the years 1980 to 2010.
Hence, the % of the increase in population from 1980 to 2000 will be [tex](\frac{1.728x - x}{x}) \times 100\% = 72.8\%[/tex] (Answer)
What is the value of p if the line that passes through (2,-4) and (p,8) has a slope of 1/2?
Answer:
Step-by-step explanation:
(2,-4)....x1= 2 and y1 = -4
(p,8).....x2 = p and y2 = 8
slope(m) = 1/2
now use the slope formula (y2 - y1) / (x2 - x1) and sub in what we know...
slope(m) = (y2 - y1) / (x2- x1)
1 / 2 = (8 - (-4) / (p - 2)
1 / 2 = (8 + 4) / (p - 2)
1/2 = 12 / (p - 2) .....now multiply both sides by (p - 2)
1/2(p - 2) = 12
1/2p - 1 = 12
1/2p = 12 + 1
1/2p = 13
p = 13 / (1/2)
p = 13 * 2/1
p = 26
so the value of p is 26
m = 3, through (1,-1)
Point-Slope
Slope intercept
Answer:
[tex]\large\boxed{y+1=3(x-1)}\\\\\boxed{y=3x-4}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - a point on a line
We have
[tex]m=3,\ (1,\ -1)\to x_1=1,\ y_1=-1[/tex]
Substitute:
[tex]y-(-1)=3(x-1)\\\\\boxed{y+1=3(x-1)}[/tex]
Convert to the slope-intercept form
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
[tex]y+1=3(x-1)[/tex] use the distributive property
[tex]y+1=3x-3[/tex] subtract 1 from both sides
[tex]\boxed{y=3x-4}[/tex]
Crater lake in Oregon is shaped like a circle with a diameter of about 5.5 miles. How far is it around the perimeter of crater lake?
Answer:
The perimeter of crater lake is 17.27 miles.
Step-by-step explanation:
Given as :
The shape of the lake is like a circle
The diameter of lake = d = 5.5 miles
∵ shape pf lake is circle, so the diameter of circle = d = 5.5 miles
Let The perimeter of crater lake = p miles
Now, As we know
The perimeter of circle = [tex]\pi[/tex] × diameter
the value of [tex]\pi[/tex] = 3.14
Or, p = [tex]\pi[/tex] × d
Or, p = [tex]\pi[/tex] × 5.5 miles
Or, p = 3.14 × 5.5 miles
∴ p = 17.27 miles
So, The perimeter of circle = perimeter of lake = p = 17.27 miles
Hence, The perimeter of crater lake is 17.27 miles. Answer
(x/(x+1) + 1)*((1+x)/(2x-1))
The question is a college-level mathematics problem involving taking the third derivative of the function f(x) = 2x/(x^2 - 1). The process requires the application of quotient rule and chain rule of differentiation.
Explanation:The student question involves calculating the third derivative of the function f(x) = 2x/(x2 - 1). This function is a rational function and can be differentiated using the quotient rule and chain rule of differentiation. Let's proceed with the derivative calculations.
First, we should recall that the function can be rewritten as:
f(x) = 2x/(x2 - 1) = 2x/[(x - 1)(x + 1)]
Now we can calculate the derivatives. For the first derivative f'(x), we use the quotient rule:
f'(x) = [(x2 - 1)(2) - (2x)(2x)]/(x2 - 1)2
For the second derivative f''(x), we differentiate f'(x) again:
f''(x) = Derivative of f'(x) with respect to x
The third derivative f'''(x) is then the derivative of f''(x). Calculations for the second and third derivatives can be a bit complex and lengthy, and it is necessary to apply the quotient rule and product rule carefully.
Through this process, we will arrive at the third derivative, f'''(x), which is what the question asks for.
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Espress 15 x^1/2 y^1/5 using a radical
Answer:
The correct answer is C. 15 ¹⁵√x⁵y³
Correct question and statement:
Express 15x^1/3 y^1/5 using a radical, as it is written in the graph attached.
Step-by-step explanation:
15x^1/3 y^1/5
15 * (x^1/3 y^1/5)
For multiplying two fractional exponents with different bases, we need to equal the denominator of the fractional exponents.
Therefore, we have:
1/3 * 5/5 = 5/15 ⇒ 1/5 * 3/3 = 3/15
15 * (x^5/15 y^3/15)
Now we can express the fractional exponents as an only radical, this way:
x^a/b = ᵇ√xᵃ
15 * ¹⁵√x⁵y³
The correct answer is C. 15 ¹⁵√x⁵y³
Which of the following is an odd function?
f(x) = x3 + 5x2 + x
O F(x)= √x
Of(x) = x2 + x
O f(x) = -x
Option 4
f(x) = -x is an odd function
Solution:
A function is odd if and only if f(–x) = –f(x)
Option 1
[tex]f(x) = x^3 + 5x^2 + x[/tex]
Substitute x = -x in above equation
[tex]f(-x) = (-x)^3 + 5(-x)^2 + (-x)[/tex]
Cubes always involve multiplying a number by itself three times, so if the number is negative the cube will always be negative
Ans squaring results in positive
[tex]f(-x) = -x^3 + 5x -x[/tex] --- eqn 1
[tex]-f(x) = -(x^3 + 5x^2 + x)\\\\-f(x) = -x^3 - 5x^2 - x[/tex] ---- eqn 2
Comparing eqn 1 and eqn 2,
[tex]f(-x) \neq -f(x)[/tex]
Therefore not an odd function
Option 2
[tex]f(x) = \sqrt{x}[/tex]
[tex]f(-x) = \sqrt{-x}[/tex]
[tex]-f(x) = - \sqrt{x}[/tex]
Therefore,
[tex]f(-x) \neq -f(x)[/tex]
Therefore not an odd function
Option 3
[tex]f(x) = x^2 + x\\\\f(-x) = (-x)^2 + (-x)\\\\f(-x) = x^2 - x[/tex]
[tex]-f(x) = -(x^2 + x) = -x^2 - x[/tex]
[tex]f(-x) \neq -f(x)[/tex]
Therefore not an odd function
Option 4
[tex]f(x) = -x\\\\f(-x) = -(-x) = x[/tex]
[tex]-f(x) = -(-x) = x[/tex]
[tex]f(-x) = -f(x)[/tex]
Thus option 4 is correct and it is an odd function
Answer:
D
Step-by-step explanation:
just took test on edge
Marissa has 10 grapes. Roger has 3 times as many grapes as Marissa. How many grapes do Marissa and Roger have in all?
Answer:
The answer is 40
Step-by-step explanation:
First, since roger has 3 times as many grapes as Marissa. do 10 times 3. The answer is 30. Roger has 30 grapes. The question is asking how much they have all together. Add 30 plus 10 and the answer that you will get is 40. The answer is 40
A number y is at least 3 and is less than 10
Answer:
[tex]3 \leqslant y < 10[/tex]
The inequality that represents the given situation is (3 ≤ y < 10).
What are inequalities?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3.So, the inequality will be:
We know that y is at least 3 and less than 10.Which means:
3 ≤ y y < 10So, the inequality will be:
3 ≤ y < 10Therefore, the inequality that represents the given situation is (3 ≤ y < 10).
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What is the value for x if 8x=12x
Answer:
x=0
Step-by-step explanation:
8x=12x
12x-8x=0
4x=0
x=0/4
x=0
kn + 4f = 9v
solve for n
Answer:
n=(9v-4f)/k
Step-by-step explanation:
kn+4f=9v
kn=9v-4f
n=(9v-4f)/k
Answer:
n = (-4f + 9v) ÷ k
Step-by-step explanation:
All you have to do is... flip the equation
Construct the graph of the equation y=kx if it is known that the point B belongs to the graph. The graph of which of these two equations goes through point M(−10, 15)?
B(2, −3)
B(3 1/3, -2)
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Answer:
The graph with B(2,-3) i.e) y=[tex]\frac{-3}{2}[/tex] x goes through the point M(-10,15).
Step-by-step explanation:
Consider M(-10,15) and given that equation is y = kx.
Now, substitute M(-10,15) in the equation
⇒ 15 = k × -10
⇒ k = [tex]\frac{15}{-10}[/tex] = [tex]\frac{-3}{2}[/tex]
⇒ y = [tex]\frac{-3}{2}[/tex] x
Now, check with the given points B(2,-3) and B([tex]3\frac{1}{3}[/tex] , -2)
1) B(2,-3)
y = [tex]\frac{-3}{2}[/tex] x
⇒(-3) = [tex]\frac{-3}{2}[/tex] × 2
⇒ -3 = -3 ⇒ LHS = RHS
⇒ B(2,-3) is the required point.
2) for b([tex]3\frac{1}{3}[/tex] , -2)
LHS ≠ RHS.
So,The graph with B(2,-3) i.e) y=[tex]\frac{-3}{2}[/tex] x goes through the point M(-10,15).
70 percent of 330 is the same as 60 percent of what number?
Answer:
yassar
Step-by-step explanation:
What is the answer yo 3x-(2y2+2
Answer:
3x-2y^2-2
Step-by-step explanation:
3x-(2y^2+2)=3x-2y^2-2
1/8x___=7/8
0 1 2 3 4 5 6 7 8 9
Answer:
1/8x___________=7/8 the answer is 6
Choose the graph below that represents the solution to the system of equations
y= 3x + 2
10x + 2y = 20
Answer:
Graph 3 represents the solution to the system of equations.
Step-by-step explanation:
The given two linear equations of x and y are
y = 3x + 2 ........ (1) and
10x + 2y = 20 .......... (2)
Now, to solve those two equations let substitute the value of y from equation (1) to the equation (2).
Hence, 10x + 2(3x + 2) = 20
⇒ 16x = 16
⇒ x = 1
And from equation (1), y = 3x + 2 = 5
Therefore, the solution of the system of equations (1) and (2) are (1,5).
Therefore, graph 3 represents the solution to the system of equations. (Answer)
Enter your answer and show all the steps that you use to solve this problem in the space provided.
Explain how mental math can be used to estimate a 15% tip on a taxi ride that costs $23.25. Find the tip using that method.
Answer:
3.75
Step-by-step explanation:
the number you want to turn into apercentage over the total value so you end up with a fraction. Then, turn the fraction into a decimal by dividing the top number by the bottom number. Finally, multiply the decimal by 100 to find the percentage.
A snowstorm dumped 22 inches of snow in 8 hours. What was the average snowfall per hour?
2.615
Step-by-step explanation:
22 divided by 8
the average snowfall per hour is 2.75 inch.
What is division?Division is the process of splitting a number or an amount into equal parts.
here, given that,
A snowstorm dumped 22 inches of snow in 8 hours.
i.e. per hour = 22/8
=2.76
hence, the average snowfall per hour is 2.75 inch.
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A television is identified by the diagonal measurement of the of screen. A television has a 36 inch screen whose height is 22 inches.what is the length of the television screen
Answer:
28.5 inches.
Step-by-step explanation:
Given: Measurement of diagonal= 36 inch.
Height= 22 inches
Picture attached to show the measurement.
As the screen of televison is measured by diagonal of screen.
∴ Hypotenous= diagonal of screen, which is 36 inches.
Now, using pythagorean theoram to find length of television screen.
[tex]hypotenous^{2} = opposite^{2}+adjacent^{2}[/tex]
∴ [tex]36^{2} = 22^{2} + adjacent^{2}[/tex]
Here adjacent is the length of television.
⇒[tex]1296= 484+ length^{2}[/tex]
Subtracting both side by 484.
⇒[tex]length^{2} = 812[/tex]
Taking square root on both side
remember: [tex]\sqrt{a^{2} } = a[/tex]
∴ [tex]length= \sqrt{812}= 28.495 \approx 28.5[/tex]
Hence, length of televison screen is 28.5 inches.
The width of a television screen can be calculated using the Pythagorean theorem. Given a diagonal of 36 inches and height of 22 inches, the approximate length of the screen is 30 inches.
Explanation:To solve this problem, we will use the Pythagorean theorem which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This principle can be written as a^2 + b^2 = c^2 where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
In the case of a television screen, the diagonal (from one corner to the opposite corner) is the hypotenuse. Given the height of the TV screen as 22 inches (one of the sides of the right triangle), and the diagonal as 36 inches (the hypotenuse), the length (the other side of the right triangle) can be found using the formula.
Let's rearrange the formula to solve for the length (b): b = sqrt(c^2 - a^2). Substitute the given measurements into the formula: length = sqrt(36^2 - 22^2), or approximately 30 inches.
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The double number line show that 4 bottles of water cost 10 dollars at a music festival.
Based in the ratio shown in the double number line, how much does 3 bottles of water cost?
Answer:
$7.50
Step-by-step explanation:
10 divided by 4 = $2.50
so, $2.50 x 3 = $7.50
Answer:
$7.5 Dollars
Step-by-step explanation:
The cost of 4 bottles is $10. So, 1 bottle is going to be $2.50 (division)
Now, to find the cost of 3 water-bottles, we have to multiply.
$2.50 * 3 = $7.50.
So, the answer to this question is 3 bottles = $7.50
(Hope this helps!)
the diameter of the larger circle is 12.5 cm. The diameter of the smaller circle is 8.5 cm. what is the approximate area of the shaded region.
PLZZZ HELP
Answer:
[tex]A=65.97\ cm^2[/tex]
Step-by-step explanation:
The complete question is
The shaded region is the area outside the smaller circle and inside the larger circle
we know that
The area of the shaded region is equal to subtract the area of the smaller circle from the area of the larger circle
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
so
The area of the shaded region is
[tex]A=\pi [r_1^2-r_2^2][/tex]
where
[tex]r_1=12.5/2=6.25\ cm[/tex] ---> radius of the larger circle (is half the diameter)
[tex]r_2=8.5/2=4.25\ cm[/tex] ---> radius of the smaller circle (is half the diameter)
assume
[tex]\pi =3.1416[/tex]
substitute
[tex]A=3.1416[(6.25)^2-(4.25)^2][/tex]
[tex]A=65.97\ cm^2[/tex]
what is the value of thi expression when d=3?
7d2+10=
A: 63
B: 52
C: 31
D: 73
Answer:
73
Step-by-step explanation:
Givens
d = 3
Equation 7d^2 + 10 = ?
Solution
7*3*3 + 10
7*9 + 10
63 + 10 = 73
if sin(x)=m, with m>0, find the value of sin(pie-x)
Answer:
Step-by-step explanation:
Sin (π - x ) = Sin x = m
Which is the number of minutes in one 24-hour day?
Answer:
there are 1,440 minutes in 24 hrs a day
Step-by-step explanation:
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The answer is 1440 if im correct
This month 9,675 people visited Hank’s web site.This is 3 times the number that visited last month.How many people visited Hank’s web site last month?
Answer:
29,025 is the answer
Step-by-step explanation:
9,675 × 3
The number of people who visited Hank's website last month is found by dividing the total visitors this month (9,675 people) by 3, resulting in 3,225 visitors last month.
Explanation:The student is faced with a mathematics problem involving division with whole numbers. The problem states that the number of people who visited Hank's website this month is three times the number of visitors from the previous month. Given that we know the number of visitors this month is 9,675, we can find out the number of visitors from the previous month by dividing this number by three.
So, the calculation is:
9675 people (this month) ÷ 3
From this calculation, we can determine that 3,225 people visited Hank's website last month.
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SCREENSHOT
When a constant force is applied to an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass 2 kg, the acceleration of the object is 35 /ms2. When the same force acts upon another object, its acceleration is 10 /ms2. What is the mass of this object?
Answer:
7 kg
Step-by-step explanation:
F=35*2=m*10
70=10m
7=m
The mass of the second object is 7 kg
First, we make the following representations
[tex]F \to[/tex] Force
[tex]a \to[/tex] acceleration
[tex]m \to[/tex] mass
The formula of force is:
[tex]F = m * a[/tex]
Since force is constant, then:
[tex]m_1 =2kg[/tex] [tex]a_1 = 35m/s^2[/tex] --- subset 1 represents the first object
[tex]m_2 = ??[/tex] [tex]a_2 = 10m/s^2[/tex] --- subset 2 represents the second object
We are to calculate the mass of the second object
A constant force means:
[tex]m_1 * a_1 = m_2 * a_2[/tex]
Make m2 the subject
[tex]m_2 = \frac{m_1 * a_1}{a_2}[/tex]
Substitute known values
[tex]m_2 = \frac{2kg * 35m/s^2}{10m/s^2}[/tex]
[tex]m_2 = \frac{2kg * 35}{10}[/tex]
[tex]m_2 = \frac{70kg}{10}[/tex]
[tex]m_2 =7kg[/tex]
Hence, the mass of the second object is 7kg
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michael has finished 25% of an art project that has taken
him a total of 4 hours so far. If he continues to work at the
same rate, how many hours will it take for him to complete
the entire project?
Annabeth, Grover, and Percy are shopping. Together, Annabeth and Grover have $43. If Grover and Percy combine their money, they have $55. Percy has $7 more than Grover. How much does each person have?
Answer:
Grover has $24, Percy has $31 and Annabeth has $19.
Step-by-step explanation:
Create equations to represent the situation.
let a be Annabeth
let g be Grover
let p be Percy
a + g = 43 Together, Annabeth and Grover have $43
g + p = 55 If Grover and Percy combine their money, they have $55
p = g + 7 Percy has $7 more than Grover
See if any of the equations can be combined. For example, we know p is g+7.
Substitute p for g+7 in an equation that has the variable p.
g + p = 55
g + g + 7 = 55 Combine like terms (g)
2g + 7 = 55 Start isolating g. Subtract 7 from both sides
2g = 55 - 7
2g = 48 Divide both sides by 2
g = 48/2
g = 24 Money Grover has
Use the equation p = g + 7. Find "p" by substituting g for 24.
p = g + 7
p = 24 + 7 Add
p = 31 Money Percy has
Substitute g for 24 in the last equation, a + g = 43, to find a.
a + g = 43
a + 24 = 43 Subtract 24 from both sides
a = 43 - 24
a = 19 Money Annabeth has
Therefore Grover has $24, Percy has $31 and Annabeth has $19.
Answer:
Grover has $24, Percy has $31 and Annabeth has $19.
Create equations to represent the situation.
let a be Annabeth
let g be Grover
let p be Percy
a + g = 43 Together, Annabeth and Grover have $43
g + p = 55 If Grover and Percy combine their money, they have $55
p = g + 7 Percy has $7 more than Grover
See if any of the equations can be combined. For example, we know p is g+7.
Substitute p for g+7 in an equation that has the variable p.
g + p = 55
g + g + 7 = 55 Combine like terms (g)
2g + 7 = 55 Start isolating g. Subtract 7 from both sides
2g = 55 - 7
2g = 48 Divide both sides by 2
g = 48/2
g = 24 Money Grover has
Use the equation p = g + 7. Find "p" by substituting g for 24.
p = g + 7
p = 24 + 7 Add
p = 31 Money Percy has
Substitute g for 24 in the last equation, a + g = 43, to find a.
a + g = 43
a + 24 = 43 Subtract 24 from both sides
a = 43 - 24
a = 19 Money Annabeth has
Therefore Grover has $24, Percy has $31 and Annabeth has $19.