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

Aniah spends a total of $22. She spends $9 on paper towels and buys 2 frozen meals. We want to find out the cost of each frozen meal.

1. Subtract the amount spent on paper towels from the total amount: \[ 22 - 9 = 13 \] This means Aniah has $13 left for the two frozen meals.

2. Since she bought 2 frozen meals that have the same cost, we divide the remaining amount by 2: \[ 13 \div 2 = 6.5 \]

Therefore, the correct sequence of steps is:

B - Subtract 9 from 22, then divide by 2.

PART B

Let's represent the cost of each frozen meal as \( x \). The total cost for 2 frozen meals is \( 2x \).

The equation based on her spending would be: \[ 2x + 9 = 22 \]

Now let's solve this step by step:

1. Subtract 9 from both sides: \[ 2x = 22 - 9 \] which simplifies to: \[ 2x = 13 \]

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

The algebraic steps leading to this solution are shown in option C:

C -
2x + 9 = 22
(Then, subtract 9 from both sides)
2x = 13
(Then, divide by 2)
x = 6.5

So the replies for the two parts are:

• Part A: B
• Part B: C