Mathematics Middle School

Tess and Dan have $24.00 each to spend at a book fair, where all students receive a 15% discount. They both want to purchase a copy of the same book, which normally sells for $24.50 plus 10% sales tax. To check if she has enough to purchase the book, Tess takes 15% of $24.50 and subtracts that amount from the normal price. She takes 10% of the discounted selling price and adds it back to find the purchase amount. Dan takes 85% of the normal purchase price and then computes 110% of the reduced price. Is Tess correct? Is Dan correct? Do they have enough money to purchase the book? Explain your answer using complete sentences, and show your work.

Answers

Answer 1

Tess is correct and Dan is incorrect

Answer 2

Answer:

Tess is wrong and Dan is correct because the tax is calculated after discount.

Step-by-step explanation:

Related Questions

Is 2/3 closer to 1 or 1/2

Answers

The 2/3 fraction would be closer to 1/2.

How to convert from decimal to fraction?

For conversion from decimal to fraction, we write it in the form a/b such that the result of the fraction comes as the given decimal. Usually, to get the decimal of the form a.bcd, we count how many digits are there after the decimal point (if its finite), then we write 10 raised to that many power as denominator, and the considered number without any decimal point as numerator.

To make them all into decimal points, which allows you to compare them easier than in fraction form. this is done by dividing the denominator by the numerator.

2/3 = 0.66

1/2 = 0.5

1 = 1.00

The answer would be closer to 1/2.

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Final answer:

When comparing 2/3 to 1 and 1/2, 2/3 is closer to 1/2 than 1.

Explanation:

When comparing the fraction 2/3 to 1 and 1/2, we can determine which it is closer to by analyzing the numerical values. To do this, we can convert both 1 and 1/2 to fractions with the same denominator as 2/3, which is 3.

1 as a fraction with a denominator of 3 is 3/3. Comparing 2/3 and 3/3, we can see that 2/3 is closer to 1 than 3/3.

On the other hand, 1/2 as a fraction with a denominator of 3 is 3/6. Comparing 2/3 and 3/6, we can see that 2/3 is closer to 1/2 than 3/6.

Therefore, we can conclude that 2/3 is closer to 1/2 than 1.

Alvin is 12 years older than Elga. The sum of their ages is 112. What is Elga's age?

Answers

Lets Elga's age = x
12 + x = Alvin
x + 12 + x = 112
2x + 12 = 112
2x = 100
x = 50

Elga's age = 50
Alvin = 50 + 12 = 62

answer
Elga's age = 50

so first you have to put up an equation x+12=112 elga's age is 100 if im not correct im very sorry

Charlott is running at a rate of 9 km/h. What is charlotte's speed in m/s?

Answers

1km = 1000m
1h = 60min = 3600s
9000m/3600s plug it into calculator

Answer:

The Charlott's speed in m/s is 2.5 m/sec

Step-by-step explanation:

Given : Charlott is running at a rate of 9 km/h.

We have to find the Charlott's speed in m/s.

Consider the given speed of Charlott is 9 km/h.

Since, 1 km = 1000 m

and 1 hour = 3600 sec

Therefore, [tex]9\frac{km}{hr}[/tex] becomes,

[tex]9\frac{km}{hr}=9\times\frac{1000\ m}{3600 \ sec}=2.5[/tex]

Thus, The Charlott's speed in m/s is 2.5 m/sec

Peter is 2 years older than Winnie. Peter's age is 16 years less than seven times Winnie's age. The equations below model the relationship between Peter's age (p) and Winnie's age (w):

p = w + 2
p = 7w − 16

Which is a possible correct method to find Peter's and Winnie's ages?

Solve w + 2 = 7w − 16 to find the value of w.
Solve p + 2 = 7p − 16 to find the value of p.
Write the points where the graphs of the equations intersect the x axis.
Write the points where the graphs of the equations intersect the y axis.

Answers

substitute P on the second equation so now it looks like...
w+2 = 7w-16. from there we can see that w = 3
So basically, the first answer.

Solve w + 2 = 7w - 16 to find the value of w.

Answer the question if you cant see all the answers it don't matter all u need is the question

Answers

I think it is D because the triangle is about 12 to 13 and the square below is about 12 too.

area for triangle = 1/2 x h x b

so 1 triangle = 1/2 x 5.12 x 3.23 = 8.2688 since the triangles are congruent they are equal so 8.2688 x 2 = 16.5376

round that up to 17

Answer is C 17 square inches

Which set of side lengths forms a right triangle??

Answers

The answer is D. 15, 36, 39.

If a^2 + b^2 =c^2, then the triangle is a right triangle

2^2 + 3^2 ??=?? 13^2
4 + 9 ??=?? 169
13 ??=?? 169 FALSE

4^2 + 6^2 ??=??10^2
16 + 36 ??=?? 100
52 ??=?? 100 FALSE

9^2 + 12^2 ??=?? 18^2
81 + 144 ??=?? 324
225 ??=?? 324 FALSE

15^2 + 36^2 ??=?? 39^2
225 + 1296 ??=?? 1521
1521 ??=?? 1521 TRUE 15, 36, 39

Correct answer gets brainliest

Answers

The answer will be C.) 70 square feet

i think 147ft hope i helped

this,is multiplication variables 2 (5x × 3y)=

Answers

the answer is 30xy. Inside is 15xy times 2 equals 30xy

In a recent year, 31.1% of all registered doctors were female. If there were 56,900 female registered doctors that year, what was the total number of registered doctors?

Answers

Your equation is

0.194*x = 43400,

where x is the unknown total number of registered doctors, which is under the question.

Solve the equation to get the answer:

x = = 223711 registered doctors.

someone help me plz.

Answers

Just do conversions, you know that there are 100 cm in a meter or you could just simply move the decimal place to the left by 2

write with fractional exponents. (do not use parenthesis) (4)√y^3)

Answers

The power rule (or law of indices) that applies to this expression is

[tex] x^{ \frac{m}{n} } = \sqrt[n]{x^{m} } = ( \sqrt[n]{x}) ^{m} [/tex]

we have [tex]4 \sqrt{ y^{3} } [/tex]
we write [tex] \sqrt{ y^{3} } = y^{ \frac{3}{2} } [/tex] , note that square root [tex] \sqrt{x} [/tex] equals to [tex] \sqrt[2]{x} [/tex]

hence, the final expression is [tex]4( y^{ \frac{3}{2} } )[/tex]

Plzzzz help me ??!?!?!??

Answers

Pythagorean Theorem is for right triangles

right triangles have a 90 degree angle in them

D is a right triangle

d is the correct answer

What is the rate of change of the linear relationship modeled in the table?

x y
1 2
3 5
5 8
7 11
(4 points)

a) negative three over two
b) two over three
c) 1
d) three over two

Answers

The slope or velocity is constant if it is a linear relationship. And that constant velocity is (y2-y1)/(x2-x1)

In this case it is (11-8)/(7-5)=(8-5)/(5-3)=etc=3/2

So the slope is 3/2.

take 2 of ur points...any 2 of them, then use the slope formula.

slope(rate of change) = (y2 - y1) / (x2 - x1)
(1,2)...x1 = 1 and y1 = 2
(3,5)...x2 = 3 and y2 = 5
now sub into the formula
slope(rate of change) = (5 - 2) / (3 - 1) = 3/2 <==

x/10+5/12= 3x-1 what is x

Answers

the answer for x is x = 85/174

Gas station A has posted a chart that shows the price of gasoline in terms of the number of gallons. Gallons Price 3 9.15 5 15.25 7 21.35 Gas station B has an equation that represents the price, p, for gallons, g, of gasoline as p = $3.08g. Which gas station sells gasoline at a lower rate? What price does it charge? Gas station A sells gasoline at a lower rate. Its price is $3.08 per gallon. Gas station B sells gasoline at a lower rate. Its price is $3.05 per gallon. Gas station A sells gasoline at a lower rate. Its price is $3.05 per gallon. Gas station B sells gasoline at a lower rate. Its price is $3.08 per gallon.

Answers

The first one sells gas at a lower rate.
Rate is $3.05

When an elderly man passed away, he had left each of his 4 children 25% of his estate If he had $72,000, how much did each child receive

Answers

Dividing $72,000 by 4, each child received $18,000

To calculate the percent of a number, we must turn the percent into its decimal form and multiply the number by it. To turn a number into a percent, you can simply move the decimal 2 places to the right. That means that 25% is equal to .25. Now, as stated, we multiply 72,000 by it. That shows that each child will get $18,000.00.

ONLY THE CORRECT ANSWERS PLEASE!!!!

Which term best represents the intersection of two pages of an open book?

A. line

B. angle

C. plane

D. point

Answers

the answer to your question is A ! I HOPE THIS HELPS

How does ray ab and ac form both a line and angle

Answers

Rays AB and AC both have a point in common. That is the A point or normally called the vertex. From the point both go in different directions making a distance between both. This distance has a degree in which it separated that forms the angle. This also forms a line because both rays, in theory, are lines. They just tend to continue to infinity in just one direction.

The steps below show the incomplete solution to find the value of x for the equation
7x − 3x − 4 = −1 + 21:

Step 1: 7x − 3x − 4 = −1 + 21
Step 2: 7x − 3x − 4 = 20
Step 3: 4x − 4 = 20

Which of these is most likely the next step?

4x = 24
4x = 16
4x = 5
4x = 80

Answers

in a problem such as this, we want to isolate the term x to one side.
therefore, the next step in the process will be to get the term "4" to the right side.
to do this, we add 4 to 20 since it is a negative.
4x=20+4

so the answer is 4x=24

hope this helps! :)

The most likely step after the step3 is 4x = 24.

Linear Equation in one variable:

The linear equation in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution.

According to the given question

we have, a linear equation in variable x, 7x - 3x -4 = -1 + 21

For solving the above equation we will do the following steps

7x -3x -4 = -1 +21

Step1: 4x - 4 = 20

Step2: 4x - 4-20= 0

Step3: 4x -24 = 0

Step4: 4x = 24

Step5: x =24/4 =6

Hence, the most likely step after the step3 is 4x = 24.

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if the area of a square is 529 in 2 , what is the length of a side of the square

Answers

The length would be 23 inches

Please help!!
Which of the following is a true statement? (round to the nearest tenth as needed)
A If 12n = -6, then n = -6
B If 12n = -6, then n = 0.5
C If 12n = -6, then n = -2
D If 12n = -6, then n = -0.5

Answers

The true statement would be A.

a. If 12n = -6 then n=-6

8x-2y-5=11 write the equation in function form

Answers

f(x,y)=8x-2y-16
In function form it all has to be on one side

Describe how you can tell that a fraction corresponds to a repeating decimal and not a terminating decimal

Answers

When a fraction corresponds to a repeating decimal, it's denominator is 9 or 99.

For example, 4/11 = 36/99 = 0.36 with bar notation over 36.

Example #2: 2/3 = 6/9 = 0.666....
or also written as 0.6 with bar notation over 6.

You know a fraction responds to a terminating decimal because it can be simplified to a terminating decimal.

Example: 2/4 = 0.5

Find the equivalent function to f(x) = 3(6)^2x

Answers

This is the concept of algebra, the function given can be written as follows;
f(x)=3(6)^(2x)
f(x)=3(6^2)^x
when we expand the above we get:
f(x)=3(36)^x
the answer is f(x)=3(36)^x

Answer:

f(x) = 3(36)x

f(x) = 182x

f(x) = 108x

f(x) = 9x(36x)

Step-by-step explanation:

The variable Z is directly proportional to X. When X is 3, Z has the value 57. What is the value of Z when X = 8

Answers

When x = 3 z = 57 57/3 = 19
19*8 = 152
So when X is equal to 8, Z is equal to 152.

A quadratic equation is shown below:

16x2 − 8x + 1 = 0

Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)

Part B: Solve 4x2 − 8x − 45 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)

Answers

First problem
We want to solve 16x² - 8x + 1 = 0

Notice that the quadratic expression is a perfect square because
(4x - 1)² = (4x)² + 2(4x)(-1) + (-1)² = 16x² - 8x + 1
Therefore
(4x - 1)² = 0
4x - 1 = 0 => x = 1/4 (multiplicity of 2)

Answer: x = 1/4 (multiplicity of 2)

Second problem
We want to solve 4x² - 8x - 45 = 0

The discriminant is
D = √[(-8)² - 4(4)(-45)]
= √784
= 28
Because D>0, there will be two real roots.

Use the quadratic formula.
x = (1/8)[8 +/- 28]
= (1/8)(36) = 4.5
or
x = (1/8)(-20)
= -2.5

Answer: x = 4.5 or x = -2.5

25(y+1)-x^2(y+1) i don't know the answer

Answers

It seems like you've begun to group and factored out the GCF.

Because the inner binomials (the ones in parentheses) are the same, the next step is to rewrite the equation like so:

(25-x^2)(y+1)

From here, we can further factor (25-x^2) since they are both perfect squares.

(5+x)(5-x)(y+1)

No further terms can be factored so that is the final answer. Hope this helps!

At 10 am, a building casts a shadow that is 98 feet long. At the same time, a 5 feet tall man casts a shadow that is 4 feet long. Find the height of the building.

Answers

the height of the building is around 122 feet

ratio and proportion

height:shadow=5:4

so

given that the shadow is 98 ft
the height of the building is?
?:98=5:4
?/98=5/4
times both sides by 98
?=490/4
?=122.5ft

te height of the building is 122.5ft

What is the solution to the following equation?

2(3x − 7) + 18 = 10

1
3
5
6

Answers

2(3x - 7) + 18 = 10
Subtract 18 from both sides.
2(3x - 7) = -8
Distribute the side with parenthesis.
2(3x) + 2(-7) = -8
6x -14 = -8
Add 14 to both sides.
6x = 6
Divide both sides by 6.
x = 1

I hope this helps!

2(3x - 7) + 18 = 10

Subtract 18 from both sides:

2(3x - 7) = -8

divide both sides by 2

3x - 7 = -4

add 7 to both sides

3x = 3

divide both sides by 3:

x = 1

So your answer is A) 1

Farmer George is painting 3 chicken coops. He started painting this morning. Now he only has 3/4 of a chicken coop left to paint this afternoon. how many chicken coops did farmer George paint this morning

Answers

Final answer:

Farmer George has painted 2 1/4 chicken coops this morning. This is calculated by subtracting the remaining part of the chicken coop(3/4) from the total chicken coops(3).

Explanation:

Farmer George had 3 chicken coops to paint in total. He only has 3/4 of one chicken coop left to paint. We can subtract the amount of work left from the total amount of work to figure out how much work he has done already.

So, if we take the total amount of chicken coops (which is 3) and subtract the remaining part that needs painting (which is 3/4), we will know how many chicken coops Farmer George has painted this morning.

The calculation is as follows: 3 - 3/4 = 2 1/4 coops

So, Farmer George completed painting 2 whole chicken coops and 1/4 of the third chicken coop this morning.

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Final answer:

Farmer George painted 2.25 chicken coops this morning. This is calculated as the total number of chicken coops (3) minus the remaining part of the chicken coop left to paint (3/4).

Explanation:

The question is asking us about how many chicken coops Farmer George painted this morning. Farmer George started with 3 chicken coops and now has 3/4 of a chicken coop left to paint. Since he's already started painting the last chicken coop, this means he has painted 2 whole coops and 1/4 of the last coop. Thus, the answer to how many chicken coops Farmer George painted this morning is 2.25 chicken coops. Mathematically, this is calculated as 3 (the total number of chicken coops) minus 3/4 (the remaining part of the chicken coop left to paint).

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