Question

Johnny Rocket purchases a new truck that had a total cost of $42,375.62 including a 6% sales tax. The

base price is $35,929 and a $800 destination charge. He had three options packages included: a winter
package including heated mirrors, seats, and steering wheel, an upgraded sound system that costs 4
times the winter package, and a style package that was 3 times the winter package. Find the cost of each
option package added.

Answer 1

Explanation:

To find the cost of each option package, we first need to subtract the cost of the base price and destination charge from the total cost, which will give us the total cost of the three option packages combined.

Base price + destination charge = $35,929 + $800 = $36,729

Total cost including sales tax = $42,375.62

Total cost of option packages = $42,375.62 - $36,729 = $5,646.62

Let's call the cost of the winter package "w." Then, we know that:

The upgraded sound system costs 4 times the winter package, or 4w.

The style package costs 3 times the winter package, or 3w.

The total cost of the three option packages is the sum of these three costs:

Total cost of option packages = w + 4w + 3w = 8w

So we have:

8w = $5,646.62

To solve for w, we divide both sides by 8:

w = $5,646.62 / 8 = $705.83

So the winter package costs $705.83. Then, we can find the cost of the other two packages:

The upgraded sound system costs 4 times the winter package, or 4 x $705.83 = $2,823.32

The style package costs 3 times the winter package, or 3 x $705.83 = $2,117.49

Therefore, the cost of each option package is:

Winter package: $705.83

Upgraded sound system: $2,823.32

Style package: $2,117.49