Write and Solve Inequalities in Context

Question

David has $520 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.

1. He buys a new bicycle for $303.93.
2. He buys 4 bicycle reflectors for $10.99 each and a pair of bike gloves for $25.25.
3. He plans to spend some or all of the money he has left to buy new biking outfits for $73.43 each.

Write and solve an inequality which can be used to determine x, the number of outfits David can purchase while staying within his budget

Answer 1

To set up the inequality you know that the total remaining money must be greater than or equal to $0. So you want to start with $520 (the total money you have available) and subtract the costs you are given. $303.93 for the bike, $10.99 (times 4) for the reflectors, and $25.25 for the gloves. Then you will subtract the costs ($73.43 each) of the outfits that he buys using a variable to solve for the maximum amount he can buy (x).

520 - 303.93 - (10.99 * 4) - 25.25 - 73.43x ≥ 0

1) Parentheses

520 - 303.93 - 43.96 - 25.25 - 73.43x ≥ 0

2) Combine like terms

146.86 - 73.43x ≥ 0

3) Get the variable term alone

-73.43x ≥ -146.86

4) Divide to solve

x ≤ 2

** Remember when dividing by a negative number, the inequality sign flips