Question

Melissa bought a new car with 12 optional features to the car. Each optional feature costs either $23.99 or $120.84. If she paid $675.28 for all the optional features, how many of each type did she buy?

Answer 1

Let us assume she bought,
`x` types of the optional features that costs $23.99

and
`y` types of the optional features that costs $120.84. Then we will have the expression,

`23.99x+120.84y`

This expression gives us the total cost which is $675.28. This implies that,

`23.99x+120.84y=675.28 --(1)`

We were told that that there were 12 optional features. That is,

`x+y=12 --(2)`

Make
`y` the subject in equation --(2).

`\Righarrow y=12-x --(3)`

Put equation (3) in equation (1).

`23.99x+120.84(12-x)=675.28`

Expand the bracket to obtain

`23.99x+1450.08-120.84x=675.28`

Group like terms,

`23.99x-120.84x=675.28-1450.08`

Simplify

`-96.85x=-774.8`

Solve for x,

`x=(-774.8)/(-96.85)=8`

Put
`x=8` in equation (3) to find
`y`.

`\Righarrow y=12-8=4`

Therefore she bought
`8` types of the optional features that costs $23.99

and
`4` types of the optional features that costs $120.84.

Answer 2

we are given with two costs of features: $23.99 or $120.84. There are 12 optional features and a total of $675.28 is paid. we translate the given into equations:

12 = x + y
$675.28 = x*$23.99 + y* $120.84

where x is number of feature 1 and y is number of feature 2\

solving the two equations,
x = 8 and
y = 4