To determine how many times the space heater would need repairs for the warranty to be worth the cost, let's first calculate the cost of the extended warranty.
The extended warranty costs 15% of the purchase price of the space heater:
\[ \text{Cost of warranty} = 0.15 \times 235 = 35.25 \]
Now, we know that each repair costs $12. To find out how many repairs would make the warranty worth the cost, we need to see how many repairs would equal or exceed the cost of the warranty ($35.25):
Let \( n \) be the number of repairs. The total cost of repairs is:
\[ \text{Total cost of repairs} = 12n \]
We want to find the smallest \( n \) such that:
\[ 12n \geq 35.25 \]
Now, divide both sides by 12:
\[ n \geq \frac{35.25}{12} \approx 2.9375 \]
Since \( n \) must be a whole number, we round up to the next whole number:
\[ n = 3 \]
Thus, the space heater must need repairs at least three times for the warranty to be worth the cost. The correct answer is:
c. three
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