Question

An electric guitar costs $830, with a $225 full-replacement warranty. If the manufacturer sells 532,475 warranties and has to honor 12% of them, how much profit did the manufacturer gain from the warranties?
a.
$105,430,050
b.
$66,772,365
c.
$53,034,510
d.
$508,726,615

Answer 1

To calculate the manufacturer's profit from the warranties, we need to follow these steps:

1. Calculate the total revenue from selling the warranties.
2. Calculate the total cost associated with honoring 12% of the warranties.
3. Subtract the total cost from the total revenue to find the profit.

### Step 1: Calculate Total Revenue from Warranties
The price of each warranty is $225, and the manufacturer sold 532,475 warranties.

\[
\text{Total Revenue} = \text{Number of Warranties} \times \text{Price per Warranty}
\]

\[
\text{Total Revenue} = 532,475 \times 225
\]

\[
\text{Total Revenue} = 119,836,875
\]

### Step 2: Calculate Total Cost of Honoring Warranties
The manufacturer has to honor 12% of the warranties. First, we find out how many warranties are honored:

\[
\text{Warranties Honored} = 532,475 \times 0.12
\]

\[
\text{Warranties Honored} = 63,897
\]

Next, we calculate the total cost to honor these warranties, assuming each warranty costs $225:

\[
\text{Total Cost} = \text{Warranties Honored} \times \text{Cost per Warranty}
\]

\[
\text{Total Cost} = 63,897 \times 225
\]

\[
\text{Total Cost} = 14,377,725
\]

### Step 3: Calculate Profit from Warranties
Now we subtract the total cost from total revenue to find the profit:

\[
\text{Profit} = \text{Total Revenue} - \text{Total Cost}
\]

\[
\text{Profit} = 119,836,875 - 14,377,725
\]

\[
\text{Profit} = 105,459,150
\]

Thus, the profit gained by the manufacturer from the warranties is approximately **$105,459,150**.

However, since none of the options (a, b, c, d) exactly match this amount, let's look for approximations based on the calculation. The option that is closest to this value is:

**a. $105,430,050**.

Hence, the correct answer is **a.**