Multiple Choice Question

Question

Sara claims that the number of pages she has read in her book is proportional to the number of minutes that she has spent reading. She collects several data points to prove her claim and expresses the data points as (x, y) coordinate pairs.

Which of the following actions could Sara take to prove her claim?

A.
Place the coordinate pairs in a table and show that they do not create equivalent ratios.

B.
Use the coordinate pairs to show that an equation of the form
can be written.

C.
List out the coordinate pairs and show that each y-value is a multiple of its associated x-value.

D.
Plot the coordinate pairs on a graph and show that the points make a straight line through the origin.

Answer 1

To prove her claim that the number of pages she has read (y) is proportional to the number of minutes she has spent reading (x), Sara would need to demonstrate that there is a consistent ratio between y and x, indicating that they are indeed proportional.

The best action she could take from the given options would be:

D. Plot the coordinate pairs on a graph and show that the points make a straight line through the origin.

This action would visually demonstrate that the relationship between the pages read and the minutes spent reading is indeed proportional since a line through the origin indicates a constant ratio (a direct variation) between the two variables.

Other options, such as A and B, do not support the claim of proportionality effectively, and option C would not conclusively demonstrate a consistent proportional relationship without further verification. Therefore, option D is the most effective choice for proving the claim.

Answer 2

Multiple Choice Question
Timothy runs a catering service for large parties. He needs 37 heads of lettuce for salad to feed 100 guests. Which of the following ratios illustrates how many heads of lettuce, x, he would need to feed 275 guests?
A.

37/100 = x/275

B.

x/100 = 37/275

C.

100/275 = x/37
D.

100/37 = x/275

Answer 3

To determine how many heads of lettuce Timothy would need for 275 guests based on the initial ratio of 37 heads for 100 guests, we can set up a proportion.

The correct way to set up the ratio is:

\[ \frac{37 \text{ heads}}{100 \text{ guests}} = \frac{x \text{ heads}}{275 \text{ guests}} \]

This setup represents the principle of proportionality, where the number of heads of lettuce is compared against the number of guests served.

Looking at the options provided:

A. \(\frac{37}{100} = \frac{x}{275}\)

This is the correct choice because it maintains the proper ratio based on the initial information.

So, the answer is A.

Answer 4

Multiple Choice Question
Christian got a haircut yesterday afternoon. If the hair stylist charged $18 and Christian gave a 20% tip, how much did he pay for the haircut?
A.
$3.60

B.
$14.40

C.
$21.60

D.
$22.60

Answer 5

To calculate the total amount Christian paid for the haircut including the tip, we first need to find the amount of the tip.

The haircut costs $18, and the tip is 20% of that amount:

\[ \text{Tip} = 0.20 \times 18 = 3.60 \]

Now, we add the tip to the cost of the haircut to find the total amount paid:

\[ \text{Total amount} = \text{Cost of haircut} + \text{Tip} = 18 + 3.60 = 21.60 \]

Therefore, the total amount Christian paid for the haircut is $21.60.

The correct answer is C. $21.60.

Answer 6

Multiple Choice Question
Janice has a pasta recipe that calls for 2 ounces of cheese for every 3 ounces of cooked pasta. Which graph shows this relationship between cheese and pasta?
A.
The graph showing 'pasta' from 0 to 10 along the x-axis and 'cheese' from 0 to 10 along the y axis showing a upward facing line starting (0, 0) and passing through the points (2, 3), (4, 6) and (6, 9).

B.
The graph showing 'pasta' from 0 to 10 along the x-axis and 'cheese' from 0 to 10 along the y axis showing a upward facing line starting (0, 0) and passing through the points (3, 2), (6, 4), and (9, 6).

C.
The graph showing 'pasta' from 0 to 10 along the x-axis and 'cheese' from 0 to 10 along the y axis showing a upward facing line starting (0, 0) and passing through the points (2, 2), (4, 4), (6, 6), (8, 8) and (10, 10).

D.
The graph showing 'pasta' from 0 to 10 along the x-axis and 'cheese' from 0 to 10 along the y axis showing a upward facing line starting (0, 0) and passing through the points (5, 2) and (10, 4).

Answer 7

To determine which graph correctly represents the relationship between cheese and pasta based on Janice's recipe where 2 ounces of cheese are used for every 3 ounces of cooked pasta, we can express this ratio mathematically.

The relationship can be expressed as:

\[ \frac{\text{cheese}}{\text{pasta}} = \frac{2}{3} \]

From this relationship, we can derive a few coordinate pairs:

1. If there are 3 ounces of pasta, there should be 2 ounces of cheese. (Point: \((3, 2)\))
2. If there are 6 ounces of pasta, there should be 4 ounces of cheese. (Point: \((6, 4)\))
3. If there are 9 ounces of pasta, there should be 6 ounces of cheese. (Point: \((9, 6)\))
4. If there are 0 ounces of pasta, there are 0 ounces of cheese. (Point: \((0, 0)\))
5. If we scale the relationship, for every additional 3 ounces of pasta added, we add 2 ounces of cheese.

Now, looking at the answer options provided:

• A: Passes through points \((2, 3)\), \((4, 6)\), and \((6, 9)\) which represents a \(3:2\) ratio in reverse. This is incorrect.

• B: Passes through points \((3, 2)\), \((6, 4)\), and \((9, 6)\), which correctly represents the \(2:3\) ratio as derived from the recipe. This is a correct representation.

• C: Passes through points \((2, 2)\), \((4, 4)\), \((6, 6)\), etc. This is not the correct ratio for cheese to pasta.

• D: Passes through points \((5, 2)\) and \((10, 4)\), which does not maintain the correct ratio.

Thus, the correct graph that shows the relationship between cheese and pasta based on Janice's recipe is:

B. The graph showing 'pasta' from 0 to 10 along the x-axis and 'cheese' from 0 to 10 along the y axis showing an upward facing line starting (0, 0) and passing through the points (3, 2), (6, 4), and (9, 6).

Answer 8

Multiple Select Question
Amy and Ben each get paid an hourly wage of $12 per hour. This week, Ben will make an additional $46 in overtime pay. They want to calculate the total amount of money they will make this week if Amy works A
hours and Ben works B
hours.

Which of the following statements are true? Select two that apply.

A.
The expression
shows the combined amount of money Amy and Ben made for their hourly work plus the overtime amount.

B.
The expression
shows the sum of the amount of money Amy made and the amount of money Ben made.

C.
The expression
shows the combined amount of money Amy and Ben made for their hourly work plus the overtime amount.

D.
The expression
shows the sum of the amount of money Amy made and the amount of money Ben made.

E.
The expression
shows the sum of the amount of money Amy made and the amount of money Ben made.

Answer 9

To determine which statements are true regarding the total earnings of Amy and Ben, we need to analyze their respective pay based on the information provided.

1. Amy's Earnings:

   • Amy works \( A \) hours at $12 per hour.
   • Therefore, Amy's earnings for the week will be \( 12A \).

2. Ben's Earnings:

   • Ben works \( B \) hours at $12 per hour.
   • His earnings for the regular hours are \( 12B \).
   • Additionally, he makes $46 in overtime.
   • Therefore, Ben's total earnings for the week will be \( 12B + 46 \).

3. Total Combined Earnings:

   • The total earnings for both Amy and Ben together will be the sum of their individual earnings: \[ \text{Total Earnings} = \text{Amy's Earnings} + \text{Ben's Earnings} = 12A + (12B + 46) = 12A + 12B + 46 \]

Now let's evaluate the statements provided:

• A. The expression shows the combined amount of money Amy and Ben made for their hourly work plus the overtime amount.
  This statement could be true if it refers to \( 12A + 12B + 46 \), but without the exact expression, we cannot confirm the accuracy.

• B. The expression shows the sum of the amount of money Amy made and the amount of money Ben made.
  This statement is true if it refers to \( 12A + 12B \), but does not take into account the overtime.

• C. The expression shows the combined amount of money Amy and Ben made for their hourly work plus the overtime amount.
  This statement is true if it refers to \( 12A + 12B + 46 \), since it includes both their regular earnings and Ben's overtime.

• D. The expression shows the sum of the amount of money Amy made and the amount of money Ben made.
  This statement is true if it represents \( 12A + (12B + 46) \) but does not include the overtime separately.

• E. The expression shows the sum of the amount of money Amy made and the amount of money Ben made.
  This may again refer to \( 12A + 12B \), which would make it true, but again not accounting for overtime.

Based on typical interpretations and assumptions of these statements, the two correct statements that refer explicitly to combined earnings (including overtime) should be those that reference the total earnings correctly:

The true statements are likely to be:

• B (as it reflects Amy's regular earnings and mentions Ben's without detailing overtime)
• C (since it specifies the combined total earnings including the overtime)

Thus, the correct selections are:

1. B
2. C

Answer 10

Multiple Choice Question
A student has 5 bags of marbles. Each bag originally contains m marbles. After adding 10 marbles to each bag, there are a total of 80 marbles. Which equation can be solved to determine how many marbles were originally in each bag?

A.

B.

C.

D.

Answer 11

To determine how many marbles were originally in each bag, we start by analyzing the information provided:

1. The student has 5 bags of marbles.
2. Each bag originally contains \( m \) marbles.
3. After adding 10 marbles to each bag, the total number of marbles becomes 80.

Let's break this down step-by-step:

• The original total number of marbles in all the bags is: \[ 5m \quad \text{(since there are 5 bags and each has } m \text{ marbles)} \]

• After adding 10 marbles to each bag, each bag now contains \( m + 10 \) marbles. Therefore, the total number of marbles now is: \[ 5(m + 10) \]

• Setting this total equal to 80 gives us the equation: \[ 5(m + 10) = 80 \]

Now, let's simplify this equation:

1. Distribute the 5: \[ 5m + 50 = 80 \]

So, the equation that can be solved to determine how many marbles were originally in each bag is: \[ 5(m + 10) = 80 \]

Without the exact equation options listed (A, B, C, D), we can't specifically choose one from them. However, the form \( 5(m + 10) = 80 \) is what you're looking for.

Please provide the options, and I can help confirm which corresponds to the derived equation!