Question

A family moves out of a home that is 1,500
square feet into a home that is 2,400
square feet.

Part A: Which expression represents the percent change in the family's home size?

Part B: What is the percent increase in square footage from the old home to the new home?

Select two answers: one for Part A and one for Part B.

Responses

B: 160%
B: 160 percent

B: 37.5%
B: 37 point 5 percent

A: 2,400−1,5001,500
A: the fraction with numerator 2 comma 400 minus 1 comma 500 and denominator 1 comma 500

B: 60%
B: 60 percent

A: 2,400−1,5002,400
A: the fraction with numerator 2 comma 400 minus 1 comma 500 and denominator 2 comma 400

A: 2,4002,400−1,500
A: the fraction with numerator 2 comma 400 and denominator 2 comma 400 minus 1 comma 500

B: 26.7%
B: 26 point 7 percent

A: 1,5002,400−1,500
A: the fraction with numerator 1 comma 500 and denominator 2 comma 400 minus 1 comma 500

Answer 1

To solve the problem, we can break it into two parts:

**Part A:** To find the expression that represents the percent change in the family's home size, we use the formula for percent change, which is given by:

\[
\text{Percent Change} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}}
\]

In this case:
- New Value = 2,400
- Old Value = 1,500

So the expression for Part A will be:

\[
\frac{2,400 - 1,500}{1,500}
\]

This corresponds to the option:
- **A: the fraction with numerator 2,400 minus 1,500 and denominator 1,500**

**Part B:** Next, we calculate the percent increase from the old home to the new home using the same formula. We can first calculate the difference and then compute the percent increase:

1. Calculate the difference in square footage:
\[
2,400 - 1,500 = 900
\]

2. Now calculate the percent increase:
\[
\text{Percent Increase} = \frac{900}{1,500} = 0.6
\]
To convert this to a percentage, multiply by 100:
\[
0.6 \times 100 = 60\%
\]

Thus, the answer for Part B is:
- **B: 60%** or **B: 60 percent**

**Final Answers:**
- Part A: **A: the fraction with numerator 2,400 minus 1,500 and denominator 1,500**
- Part B: **B: 60%** or **B: 60 percent**