A new cell phone has a purchase price of $225. With the extended warranty, the total cost comes to $289. What percent of the purchase price is the price of the warranty?

Question

a.
28%
b.
22%
c.
25%
d.
20%

Answer 1

To determine the percentage of the purchase price that the warranty costs, we first need to find the cost of the warranty.

1. Subtract the purchase price from the total cost with the warranty: $$\text{Cost of warranty}=\text{Total cost}-\text{Purchase price}=289-225=64$$

2. Next, calculate the percentage of the purchase price that the warranty represents: $$\text{Percentage}=\left(\frac{\text{Cost of warranty}}{\text{Purchase price}}\right)\times 100$$ $$\text{Percentage}=\left(\frac{64}{225}\right)\times 100$$ $$\text{Percentage}\approx 28.44$$

Rounding 28.44% gives us approximately 28%. Thus, the cost of the warranty as a percentage of the purchase price is:

a. 28%