Aniyah goes to the store and spends $22. She spends $9 on paper towels and she buys 2 frozen meals that have the same cost.

Question

PART A

Which of the following sequences of steps can be used to find the cost of each frozen meal?

Responses
A Multiply 9 by 2, then subtract the result from 22Multiply 9 by 2, then subtract the result from 22
B Subtract 9 from 22, then divide by 2Subtract 9 from 22, then divide by 2
C Divide 22 by 2, then subtract 9Divide 22 by 2, then subtract 9
D Subtract 9 from 22, then subtract 2Subtract 9 from 22, then subtract 2
Question 2
PART B

Which of the following shows the algebraic steps used to write and solve an equation to determine the cost of each frozen meal?

Responses
A












2 times open paren x plus 9 close paren is equal to 22 the fraction with numerator 2 times open paren x plus 9 close paren and denominator 2 is equal to 22 halves x plus 9 is equal to 11 negative 9 is equal to negative 9 x is equal to 2
B












2 x plus 9 is equal to 22 2 x over 2 plus 9 is equal to 22 halves x plus 9 is equal to 11 negative 9 is equal to negative 9 x is equal to 2
C












2 x plus 9 is equal to 22 negative 9 is equal to negative 9 2 x is equal to 13 2 x over 2 is equal to 13 halves x is equal to 6 point 5
D

2 x plus 9 is equal to 22 negative 9 is equal to negative 9 2 x is equal to 13 negative 2 is equal to negative 2 x is equal to 11
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Answer 1

Let's break down the problem step-by-step.

PART A: Aniyah spends a total of $22. She spends $9 on paper towels and buys 2 frozen meals that have the same cost. To find the cost of each frozen meal, you can follow these steps:

1. Subtract the amount spent on paper towels from the total spent: \[ 22 - 9 = 13 \]

2. Divide the remaining amount (which is the total spent on the frozen meals) by 2 to find the cost of each meal: \[ \frac{13}{2} = 6.5 \]

So, the correct sequence of steps is: B: Subtract 9 from 22, then divide by 2.

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PART B: Now let's write and solve an equation based on the information. Let \( x \) be the cost of each frozen meal. Since Aniyah buys 2 frozen meals, we can express the situation with the equation:

\[ 2x + 9 = 22 \]

Next, to solve for \( x \):

1. Subtract 9 from both sides: \[ 2x = 22 - 9 \] \( 2x = 13 \)

2. Divide both sides by 2: \[ x = \frac{13}{2} \] \( x = 6.5 \)

Now, reviewing the options:

• Option A has the wrong equation setup.
• Option B states \( 2x + 9 = 22 \), followed by appropriate steps to find \( x = 6.5 \). This is correct.
• Option C also has incorrect intermediate steps.
• Option D includes incorrect operations leading to the wrong result.

So, the correct set of algebraic steps is: B: 2x + 9 = 22 followed accurately to find \( x \).

In conclusion:

• Part A: B
• Part B: B