Paint costing $19 per gallon is to be mixed with thinner costing $3 per gallon. How much of each should be added to make 16 gallons of a mix that costs $14 per gallon?

Answers

Answer 1
Final answer:

To make a 16-gallon mix that costs $14 per gallon from a paint costing $19 per gallon and a thinner costing $3 per gallon, you need approximately 11.56 gallons of paint and 4.44 gallons of thinner.

Explanation:

This is a problem of Mathematics, specifically Systems of Equations. Let's denote the amount of paint as P (in gallons) and the amount of thinner as T (in gallons). We are looking for the values of P and T that satisfy these two conditions:

P + T = 16 (The total volume of the solution should be 16 gallons)19P + 3T = 14 * 16 (The total cost of the solution should be $14 per gallon)

This gives us two equations,

P + T = 1619P + 3T = 224

Now, you can subtract the first equation from the second to solve for P,

18P = 208, therefore P = 208/18 = 11.56 gallons. Substitute P = 11.56 into the first equation to solve for T, T = 16 - 11.56 = 4.44 gallons. So, approximately 11.56 gallons of paint and 4.44 gallons of thinner should be mixed to get the desired 16-gallon mixture.

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Answer 2

To find the amounts of paint and thinner needed to make a $14 per gallon mix by mixing two different-priced liquids.

Mathematically, this problem can be solved using a system of equations.

Let x be the gallons of paint and y be the gallons of thinner. We have two equations based on the given information:

x + y = 1619x + 3y = 14 * 16

Solving this system of equations will give you the amounts of paint and thinner that need to be mixed to achieve a $14 per gallon mix.


Related Questions

An industrial kitchen makes a batch of trail mix containing 52.85 pounds of granola, and 13.4 pounds each of four other ingredients. The batch of trail mix is then distributed equally into five storage containers. How much trail mix is in each storage container?

Answers

There is 21.29 pounds in each storage container.

Answer:

There is 21.29 pounds of trail mix in each container.

Step-by-step explanation:

An industrial kitchen makes a batch of trail mix containing 52.85 pounds of granola, and 13.4 pounds each of four other ingredients.

Total ingredients used =[tex]52.85+4(13.4)[/tex]

= 106.45 pounds

The batch of trail mix is then distributed equally into five storage containers.

Hence, each container contains = [tex]\frac{106.45}{5}=21.29[/tex] pounds of trail mix.

There is 21.29 pounds of trail mix in each container.

Find the domain and range of the relation, and determine whether it is a function.
{(2, 1), (−4, 5), (1, 7), (2, −3), (−1, 2)}

Answers

The domain is all the x values so {2,-4, 1, 2, -1} 
The range is all the y values so    {1, 5, 7, -3, 2}

Yes, it is a function because each item in the domain matches one item in the ranges. 

The domain and range of the relation will be [−4, −1, 1, 2, 2] and [−3, 1, 2, 5, 7], respectively. The relation is a function.

What are domain and range?

The domain means all the possible values of x and the range means all the possible values of y.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The function is given in the form of a coordinate.

f = {(2, 1), (−4, 5), (1, 7), (2, −3), (−1, 2)}

The domain of the function will be


D = [−4, −1, 1, 2, 2]

And the range of the function will be

R = [−3, 1, 2, 5, 7]

The domain and range of the relation will be [−4, −1, 1, 2, 2] and [−3, 1, 2, 5, 7], respectively.

The relation is a function because the values of the ordinate are different.

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K=1/2 mv^2. Determine m when v=30 and k=4500

Answers

[tex]K=\frac{1}{2}mv^2[/tex]

when v=30 and k=4500
[tex]4500=\frac{1}{2}m(30)^2[/tex]
[tex]4500=\frac{1}{2}m900[/tex]
[tex]4500=450m[/tex]
divide bot sides by 450
[tex]10=m[/tex]


m=10
k = 1/2mv^2.....v = 30, k = 4500

4500 = 1/2m30^2
4500 * 2 = 900m
9000 = 900m
9000/900 = m
10 = m <==


3,817,773 rounded to nearest 100,000

Answers

3,800,000 is the answer
Final answer:

To round 3,817,773 to the nearest 100,000, you look at the digit in the thousands place, which is 1. Since the digit in the hundreds place (7) is greater than or equal to 5, you round up. So, 3,817,773 rounded to the nearest 100,000 is 3,800,000.

Explanation:

To round 3,817,773 to the nearest 100,000, we look at the digit in the thousands place, which is 1. Since the digit in the hundreds place (7) is greater than or equal to 5, we round up. We change the digit in the thousands place to 2 and set all the digits to the right of it to 0. So, 3,817,773 rounded to the nearest 100,000 is 3,800,000.

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you have scored 7,10,8 , and 9 on four quizzes . write and solve an equation to find the score you need on the fifth quiz so that your mean score is 8

Answers

You have scored 7, 10, 8, and 9 on four quizzes. You are trying to find the score you need on the fifth quiz so that your mean score is 8. The definition of means is to add all of the numbers and divide them by how many numbers you added. Therefore, 7+10+8+9 = 34. You need to add the fifth score, which will be "x". (34+x)/5 = 8. 34 + x = 40. x = 6. Thus, your answer is 6.
Final answer:

To achieve a mean score of 8 after five quizzes, you would need to score 6 in your fifth quiz, assuming your scores in the first four quizzes were 7, 10, 8, and 9 respectively.

Explanation:

Yes, these scores are associated with the subject of mathematics, particularly the branch of math known as statistics. This involves determining how to achieve a desired mean, which in this case is 8, given your previous quiz scores.

The mean score is determined by adding all your quiz scores together and dividing by the total number of quizzes. So for your first four quizzes, the total is 7 + 10 + 8 + 9 = 34. The mean so far is 34 ÷ 4 = 8.5 which is already above our targeted mean of 8.

To achieve a mean of 8 over 5 quizzes, the total of your scores would need to be 8 x 5 = 40. Therefore, the score you would need to get on your fifth quiz would be 40 (the desired total) - 34 (the current total) = 6.

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Mischa dives from a platform that is 10 meters above the water. Her dive takes her 2.3 meters below the surface of the water. How far does Mischa's dive take her?

Answers

12.3 meters because of the 10 meters she jumped plus the 2.3 she went down equals 10+2.3=12.3

Answer:

12.3 meter.

Step-by-step explanation:

Mischa dives from a platform that is 10 meters above the water.

Her dive takes her 2.3 meters below the surface of the water.

The total distance of Mischa's dive take her = 10 + 2.3

                                                                         = 12.3 meters.

Mischa's dive takes her 12.3 meter.

simplicity the expression (0.4^3)

Answers

0.4^3 = 0.4 * 0.4 * 0.4 = 0.064
(0.4^3) = (0.4)(0.4)(0.4) = 0.064

hope it helps

Given that 1 meter = 1 x 109 nanometers, what is the diameter of the average cell in the human body, in nanometers? Show your work


The diameter of the average cell in the human body is 1 x 10-5 meters

Answers

This is a conversion problem (meters to nanometers) so all you do is use the values given to you in the question.

We know that 1 meter = 1*10^9 nanometers, meaning that for every one meter is also 1*10^9 nanometers and vice versa. So we can set up the "train tracks"
[
tex] \frac{1*10^9 nanometers}{1 meter} * (1*10^-5 meters) [/tex]
I set it up that way because it cancels out the units "meters" since 1 meter is in the denominator and the other meter is in the numerator.

Then I'll be left with: [tex] \frac{1*10^9 nanometers}{1} * (1*10^-5 ) [/tex]
Now we can solve as is. 
[tex] \frac{1*10^9 nanometers}{1} * (1*10^-5) = 10000 nanometers [/tex]

if Johnny has 3 apples and he gives Tom one apple how many apples does Johnny have

Answers

2 apples 3-1=2 because if you have 3 apples and tom takes 1 do the math 1-3 you're answer is 2
3-1=2
He has 2 apples

Finding multiples that go into 86 52 18

Answers

do you need the GCF or LCM the GCF is 2 the LCM is 20124

Lillian bought 2.52 pounds of tomatoes and 1.26 pounds of lettuce to make salad for 18 people. If each person got the same amount of salad , how much salad did each person get?

Answers

Answer:

amount of salad by each person  = 0.21  pounds

Step-by-step explanation:

Lilian bought 2.52 pounds of  tomatoes and 1.26 pounds of lettuce to make salad for 18 people.  That means the combined weight in pounds of tomatoes and lettuce is the weight of the salad.

The weight of the salad = 2.52 + 1.26

The weight of the salad = 3.78  pounds

The total weight of the salad is 3.78 pounds . He shared the weight to 18 people and each person collected the same amount.

To find the amount each person got, we divide 3.78 by 18 people.

amount of salad by each person = 3.78/18

amount of salad by each person  = 0.21  pounds

Evaluate.
2 × ((4^2)^-1)
PLEASE HELP
A. 1/2

B. 1/4

C. 1/8

D. 1/16

Answers

2 * ((4^2)^-1)
2*(16^-1)
2*(1/16)
2/16
1/8

Hope this helps!

Monique needs to buy a baseball for $20, a soccer ball for $15, and a set of tennis balls for $12. Monique has a coupon that gives her a discount of x percent on a baseball. She has a second coupon that gives her a discount of y percent on a set of tennis balls. The third coupon gives her a discount of z percent on her total purchase. She cannot combine the coupon for the total purchase with the other two coupons. These expressions give both possibilities for the total cost of Monique's purchase after the coupons are applied, the variables represent the percentages as decimals. (1−x)20+(1−y)12+15 (1−z)(20+15+12) Which part of the expression represents the price of the set of tennis balls after a coupon was applied directly to them?

a.)12

b.)12(1−y)

c.)20 + 15 + 12

​ d.)20(1−x) ​

Answers

b is the only answer because its the only one directly applying a discount on the tennis balls 

Answer:

[tex]12(1-y)[/tex] represents the price of the set of tennis balls after a coupon was applied.

Step-by-step explanation:

Monique needs to buy a baseball for $20, a soccer ball for $15, and a set of tennis balls for $12.

In the given expression, [tex](1-x)20+(1-y)12+15[/tex] ; [tex](1-y)12[/tex] represents the price of the set of tennis balls after a coupon was applied.

Because the second coupon gives her a discount of y percent on a set of tennis balls and the cost of the set is $12.

The expression 625(1−x) gives the discounted price of a television, where x is the percent of the discount written in decimal form.

What does the 625 represent in the expression?

the original price of the television

the percent of the original price being paid

the discounted price of the television

the percent of discount

Answers

the original price of the television

is your answer.

Let

x------->  the percent of the discount written in decimal form.

y-------> the discounted price of the television

we know that

[tex]y=625(1-x)[/tex]

In the expression

[tex]625[/tex]-------> represent the original price of the television

y--------> the discounted price of the television

x-------> the percent of discount

therefore

the answer is the option

the original price of the television

A group of 5 friends are sharing 2 pounds of trail mix . Write a division problem and a fraction to represent this situation

Answers

6.4 there's 16 ounces in a pound thats 32 ounces so divide that by 5 =6.4 
2 ÷ 5
2/5
Each friend gets 40% of the bag, btw

How do u do this math question

Answers

There are 360 degrees in this shape so:

360-140-70-110 = 40

Hope this helped

N=6 times 35+4 ???? Can Someone Plz Help Me

Answers

Use PEMDAS, and multiplication comes first so 35×6=210. Then add 210+4, which will give you n=214
N=(6)(35)+4
N=210+4
N=(210+4)
N=214



the density of gold is 19.3g/cm3. if I have a nugget with a volume of 10 cm3, what is the mass of the cube?

Answers

Mass= Density•Volume
M=19.3g/cm3• 10cm3
M=193g

The measures of three sides of a triangle can be represented by 2x, 3x and -5, and 4x + 2. The perimeter of the triangle is 65 inches.
a) give an equation to represent this situation.
b) solve for x
c) What are the three lengths of a triangle?

Answers

the sides are 2x, 3x-5 and 4x+2
perimiter is the sum of the sides

a.
2x+3x-5+4x+2=63 is an equation

b.
solve
group like terms
2x+3x+4x-5+2=65
add like terms
9x-3=65
add 3 to both sides
9x=68
divide both sides by 9
x=68/9


2x=2(68/9)=136/9 in
3x-5=3(68/9)-5=(68/3)-5=(68/3)-(15/3)=53/3
4x+2=4(68/9)+2=272/9+2=272/9+18/2=290/9

the side lengths are 136/9in, 53/3in, and 290/9in

3 apples cost $1.26 how much do 10 apples cost

Answers

3 apples cost $1.26. To find the price of how much 10 apples cost, we need to know how much one apple costs. To find that, divide 1.26 by 3.[tex] \frac{1.26}{3}=0.42 [/tex]

That means that one apple is $0.42. Cool! So now, to find how many 10 apples costs, we need to multiply by 10. 

[tex]0.42*10=$4.20[/tex]

10 apples costs $4.20! 
The correct answer is $4.20.

How many places to the left did you move the decimal point to write 41,200 in scientific notation

Answers

4 since there are 4 digits to move the decimal

fill the table using this function rule.

y =29-2x

x y

1 ?
3 ?
4 ?
5 ?

Answers

y=29-2(1)
y=29-2=27
(1,27)
y=29-2(3)
y=29-6=23
(3,23)
y=29-2(4)
y=29-8=21
(4,21)
y=29-2(5)
y=29-10=19
(5,19)

PLEASE ANSWER OR ILL FAIL MATH


A seafood restaurant claims an increase of $3,150 over its average profit during a week where it introduced a special of baked clams.



Part 1
If this is true, how much extra profit did it receive per day?

The restaurant received $
450
extra profit per day.


Part 2
If it had, instead, lost $150 per day, how much money would it have lost for the week?

The restaurant would have lost $
1,050
for the week.


Part 3 out of 3
If its total loss was $420 for the week, what was its average daily change?

The restaurant's average daily change was −$
.

Answers

Final answer:

The restaurant gained an additional $450 per day with the special item, lost $1,050 if it had lost $150 per day, and an average daily loss of $60 if the total weekly loss was $420.

Explanation:

To calculate the extra profit per day, we divide the total extra profit by the number of days in a week. $3,150 divided by 7 days gives us $450 extra profit per day.

If the restaurant had lost $150 per day instead, we would multiply the daily loss by the number of days in a week. So, $150 times 7 days equals a total loss of $1,050 for the week.

For the last part, if the total loss for the week was $420, to find the average daily change, we divide this amount by 7. Thus, $420 divided by 7 days equals a daily change of -$60.

Mr Grant needs 30 pieces of felt. He can buy them in packs of 10 or as single pieces. What are the different ways Mr Grant can buy felt?

Answers

Grant can buy 3 packes of the 10 or he can put 30 packs of the single pieces
Grant can but 3 packs of 10, 30 single pieces, or 2 packs of 10 single pieces

which decimal is least in value
0.511 0.57 0.453 0.582

Answers

0,453 is the answer
0.453, 0.511, 0.57, 0.582
smallest to greatest values

I need help with number 4

Answers

So you first want to move all variables to one side.

2x = 1/8 + 4x

So perform the opposite of each operation to move it.

2x - 4x = 1/8 + 4x - 4x

-2x = 1/8

And then just divide both sides by -2

-2x / -2 = 1/8 / -2

x = -1/16

In the figure, GK (with an arrow pointing right) bisects angle FGH.

(L = angle)

if mL FGK = 3v - 4 AND mL KGH = 2v +7

a) 33
b) 58
c) 11
d) 29

Answers

mL FGK = 3v - 4 AND mL KGH = 2v +7

mL FGK = mL KGH 

3v - 4 =  2v + 7
-2v         -2v


v - 4 = 7
  +4   +4

v = 11

Use the formula for the area of a rectangle A=lw to answer the question. A rectangle has a width of n units. Its length is 4 units longer than the width. What is the area of the rectangle? A) 2n+4
B) 2+4n
C) 4n
D) n(n+4)

Answers

the area of a rectangle is its length times it width. we know the width is n and the length is n + 4. Therefore the answer is d- n(n+4)
The answer is D. N(n+4)
Hope this helps.

Defined as bounded by two distinct end points that contain every point on the line between its end points.
A) circle Eliminate
B) line segment
C) parallel lines
D) perpendicular lines

Answers

Answer:

line segment

Step-by-step explanation:

the formula for the perimeter of a rectangle is P=2l, + 2w, where l is the length and w is the width. A rectangle has a perimeter of 24 inches. Find it's dimensions if it's length is 3 inches greater than it's width.

Answers

P = 24 inches
w = x
l = 3 + x

P = 2l + 2w
24 = 2(3+x) + 2(x)
24 = 6 + 2x + 2x
24 = 6 + 4x
24 - 6 = 4x
18 = 4x
18/4 = x
4.5 = x
x = 4.5

Therefore, w = 4.5 inches and l =  7.5 inches

The dimensions of the rectangle are 7.5 inches and 4.5 inches, or w = 4.5 inches and l =  7.5 inches if the perimeter of a rectangle is P=2l, + 2w.

What is the area of the rectangle?

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

The rectangle can be defined as the two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.

P = 24 inches

l = 3 + w

P = 2l + 2w

24 = 2(3 + w) + 2w

24 = 6 + 2w + 2w

24 = 6 + 4w

24 - 6 = 4w

18 = 4w

w = 4.5 inches

l = 3 + 4.5 = 7.5 inches

Thus, the dimensions of the rectangle are 7.5 inches and 4.5 inches, or w = 4.5 inches and l =  7.5 inches if the perimeter of a rectangle is P=2l, + 2w.

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