Question

A space heater costing $235 offers an extended warranty for 15% of the purchase price. If the local repair shop will fix a space heater for $12, how many times must the space heater need repairs for the warranty to be worth the cost?

1) Less than 2 times
2) 2 times
3) More than 2 times
4) Cannot be determined

Answer 1

The space heater must be repaired more than 2 times for the extended warranty, costing 15% of the purchase price, to be cost-effective compared to the local repair shop's fixed fee of $12 per repair.

Step-by-step explanation:

The question is asking how many times a space heater would need repairs for the extended warranty, which costs 15% of its purchase price, to be worth the cost compared to having the repairs done at a local repair shop at a fixed price per repair.

First, we calculate the extended warranty cost:

• Extended warranty = 15% of $235
• Extended warranty = 0.15 × $235
• Extended warranty = $35.25

Next, we compare this cost to the repair cost at the local shop:

• Repair cost = $12 per repair
• Number of repairs at which warranty's cost is equal to repair costs: $35.25 / $12 ≈ 2.94

Therefore, the number of repairs needed for the warranty to be worth the cost is more than 2. This means that the space heater must be repaired more than 2 times for the warranty to be cost-effective.