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 a 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%.

Explanation:

Step1: Calculate percent change for first guitar

Percent change formula: $\text{Percent Change} = \frac{\text{Original Price} - \text{Sale Price}}{\text{Original Price}} \times 100\%$
For first guitar: Original = $160$, Sale = $100$
$\frac{160 - 100}{160} \times 100\% = \frac{60}{160} \times 100\% = 37.5\%$

Step2: Calculate percent change for second guitar

For second guitar: Original = $250$, Sale = $150$
$\frac{250 - 150}{250} \times 100\% = \frac{100}{250} \times 100\% = 40\%$

Step3: Compare percent changes

First guitar: $37.5\%$, Second guitar: $40\%$
So second guitar has greater percent change.

Answer:

The second guitar has a greater percent change of approximately 40%. (Corresponding option: The second guitar has a greater percent change of approximately 40%.)