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,

$x=\frac{-774.8}{-96.85}=8$

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