Question

Shane and Abha earned a team badge that required their team to collect no less than 2000 cans for recycling. Abha collected 178 more cans than Shane did. Write an inequality to determine the number of cans, S, that Shane could have collected. What is the solution set of the inequality? Also, What is the solution set of the inequality?

Answer 1

`2S+178\ge 2,000,`

`[911,\infty).`

Explanation:

Let S be the number of cans that Shane had collected.

Abha had collected 178 more cans than Shane did, then Abha had collected S+178 cans.

Shane and Abha earned a team badge that required their team to collect no less than 2000 cans for recycling, this means that

`S+S+178\ge 2,000,\\ \\2S+178\ge 2,000.`

Solve this inequality:

1. Divide it by 2:

`S+89\ge 1,000.`

2. Now

`S\ge 1,000-89,\\ \\S\ge 911.`

The solution set is
`[911,\infty).`