Question

Betty Richard's new sedan has a $43,895.60 MSRP including title and processing fees. The navigation system cost twice as much as the upgraded sound system, which included AM/FM stereo with CD/MP3 player, and 9

speakers. Including the 6.5% sales tax, the total cost of her new car was $48,346.31. Find the cost of the a)
upgraded sound system, and b) navigation system.

Answer 1

9514 1404 393

Answer:

a) sound system: $500

b) navigation system: $1000

Explanation:

The cost of the car with its upgrades (before tax) is ...

$48,346.31/1.065 = 45,395.60

This means the total cost of the sound and navigation upgrades is ...

$45,395.60 -43,895.60 = $1500

The ratio of sound system cost to navigation system cost is 1 : 2, so the sound system accounts for 1/(1+2) = 1/3 of the cost of the upgrades.

a) The upgraded sound system cost is 1/3 × $1500 = $500.

b) The upgraded navigation system cost is 2/3 × $1500 = $1000.