Question

Angela bought two pairs of shoes for a total of $138$ The difference in the price of shoes was $42. How much was the more expensive pair of shoes? Use systems of equations to solve. You must use substitution to solve

Answer 1

$90

Explanation:

Variable x = Less Expensive Shoe

Variable y = More Expensive Shoe

Set up equations:

x + y = 138

x + 42 = y

The problem says to use substitution to solve, meaning we must substitute one variable for a different value. I will substitute variable y in the first equation for x + 42 as this equals y in the second equation.

x + x + 42 = 138

Combine like terms

2x + 42 = 138

Subtract both sides by 42 to isolate variable x

2x = 96

Divide both sides by 2 to isolate variable x

x = 48

Substitute variable x for 48 and solve for y. I will use the second equation for this.

48 + 42 = y

Combine like terms

90 = y

I defined y as the more expensive pair of shoes. Since the problem only asks for the price of the more expensive shoes, the answer is $90.