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?

Question

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%."