Question

A vacuum cleaner costs $68, and the full-replacement extended warranty costs $22. If the manufacturer sells 360,920 vacuum cleaners under warranty and must replace 15% of them to honor the warranties, how much will the replacement costs be?
a.
$4,258,856
b.
$3,681,384
c.
$1,191,036
d.
$6,749,204

Answer 1

To find the replacement costs for the vacuum cleaners under warranty, we can follow these steps:

1. Find the number of vacuum cleaners that need to be replaced.
2. Multiply that number by the cost of each replacement vacuum cleaner.

### Step 1: Calculate the number of vacuum cleaners that need to be replaced.

Given that the total number of vacuum cleaners under warranty is 360,920 and 15% of them need to be replaced, we can calculate:

\[
\text{Number of replacements} = 360,920 \times 0.15
\]

Calculating that:

\[
\text{Number of replacements} = 360,920 \times 0.15 = 54,138
\]

### Step 2: Calculate the total replacement costs.

Each replacement vacuum cleaner costs $68, so the total replacement costs will be:

\[
\text{Total replacement costs} = \text{Number of replacements} \times \text{Cost per replacement}
\]

Calculating that:

\[
\text{Total replacement costs} = 54,138 \times 68
\]

Calculating that gives:

\[
\text{Total replacement costs} = 3,681,384
\]

### Conclusion

The total replacement costs will be **$3,681,384**.

So, the correct answer is **b. $3,681,384**.