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

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kudzordzifrancis kudzordzifrancis · Answer 2 · 2018-10-05T05:25:13-04:00

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

and @@MATH_TOKEN_1@@ 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,

@@MATH_TOKEN_3@@

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

@@MATH_TOKEN_4@@

Make @@MATH_TOKEN_5@@ the subject in equation --(2).

@@MATH_TOKEN_6@@

Put equation (3) in equation (1).

@@MATH_TOKEN_7@@

Expand the bracket to obtain

@@MATH_TOKEN_8@@

Group like terms,

@@MATH_TOKEN_9@@

Simplify

@@MATH_TOKEN_10@@

Solve for x,

@@MATH_TOKEN_11@@

Put @@MATH_TOKEN_12@@ in equation (3) to find @@MATH_TOKEN_13@@.

@@MATH_TOKEN_14@@

Therefore she bought @@MATH_TOKEN_15@@ types of the optional features that costs $23.99

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