Question

Carey is trying to decide between two guitars. The first had an original price of $160, but is on sale for $100. The second had an original price of $250, but is on sale for $150. Which guitar has a greater percent change in price?
The first guitar has greater percent change of approximately 35%.
The second guitar has a greater percent change of approximately 40%.
The first guitar has a greater percent change of approximately 54%.
The second guitar has a greater percent change of approximately 67%.

Answer 1

To determine which guitar has a greater percent change in price, we can calculate the percent change for each guitar using the formula:

\[
\text{Percent Change} = \left( \frac{\text{Original Price} - \text{Sale Price}}{\text{Original Price}} \right) \times 100
\]

Let's calculate the percent change for both guitars:

**First Guitar:**
- Original Price: $160
- Sale Price: $100

\[
\text{Percent Change} = \left( \frac{160 - 100}{160} \right) \times 100
\]

\[
= \left( \frac{60}{160} \right) \times 100
\]

\[
= 0.375 \times 100
\]

\[
= 37.5\%
\]

**Second Guitar:**
- Original Price: $250
- Sale Price: $150

\[
\text{Percent Change} = \left( \frac{250 - 150}{250} \right) \times 100
\]

\[
= \left( \frac{100}{250} \right) \times 100
\]

\[
= 0.4 \times 100
\]

\[
= 40\%
\]

Now we compare the percent changes:
- First Guitar: 37.5%
- Second Guitar: 40%

Thus, the second guitar has a greater percent change in price of approximately 40%. Therefore, the correct option is:

"The second guitar has a greater percent change of approximately 40%."