Question

Shane and Abha earned a team badge that required their team to collect no less than 20002000 cans for recycling. Abha collected 178178 more cans than Shane did.

Write an inequality to determine the number of cans, SS, that Shane could have collected.

What is the solution set of the inequality?

Answer 1

Answer: Inequality for the number of cans Shane collected is .Solution set of the inequality is .

Answer 2

Inequality is
`2x+178\geq 2000`.

Solution set is
`x\geq 911`.

Explanation:

Let the number of cans collected by Shane = x and the number of cans collected by Abha = y.

It is given that, Abha collected 178 cans more than Shane.

So, we have,
`y=x+178`.

Since, they both have to collect cans no less than 2000 i.e. greater than or equal to 2000.

So, the equation representing the situation is,

Shane + Abha ≥ 2000

i.e. y + x ≥ 2000

i.e.
`x+178+x\geq 2000`

i.e.
`2x+178\geq 2000`

i.e.
`2x\geq 2000-178`

i.e.
`2x\geq 1822`

i.e.
`x\geq 911`

Thus, we have,

Inequality for the number of cans Shane collected is
`2x+178\geq 2000`.

Solution set of the inequality is
`x\geq 911`.