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?

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

Answer Link

kudzordzifrancis kudzordzifrancis · Answer 2 · 2018-10-05T11:25:13+02:00

Let us assume she bought, [tex]x[/tex] types of the optional features that costs $23.99

and [tex]y[/tex] types of the optional features that costs $120.84. Then we will have the expression,

[tex]23.99x+120.84y[/tex]

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

[tex]23.99x+120.84y=675.28 --(1)[/tex]

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

[tex]x+y=12 --(2)[/tex]

Make [tex]y[/tex] the subject in equation --(2).

[tex]\Righarrow y=12-x --(3)[/tex]

Put equation (3) in equation (1).

[tex]23.99x+120.84(12-x)=675.28[/tex]

Expand the bracket to obtain

[tex]23.99x+1450.08-120.84x=675.28[/tex]

Group like terms,

[tex]23.99x-120.84x=675.28-1450.08[/tex]

Simplify

[tex]-96.85x=-774.8[/tex]

Solve for x,

[tex]x=\frac{-774.8}{-96.85}=8[/tex]

Put [tex]x=8[/tex] in equation (3) to find [tex]y[/tex].

[tex]\Righarrow y=12-8=4[/tex]

Therefore she bought [tex]8[/tex] types of the optional features that costs $23.99

and [tex]4[/tex] types of the optional features that costs $120.84.