Question

A recycling center pays $0.10 per aluminum can and $0.05 per plastic bottle. The Cheerleading squad wants to raise $500. Let x represent aluminum cans and y represent plastic bottles. Use this description to answer all questions in this section.

Answer 1

Question:

(a) Write a linear equation that describes the problem

(b). If the cheerleading squad collects 6000 plastic bottles, how many cans will it need to collect to reach the goal?

Answer:

a.
`0.10x + 0.05y = 500`

b. 2000 cans

Explanation:

We have the following:

`Cost = \$0.10` per aluminum

`Cost = \$0.05` per plastic bottle

`Total = \$500`

Solving (a): The linear equation.

If 1 aluminum can costs $0.10,

x cans would cost $0.10x

If 1 plastic bottle costs $0.05,

y bottles would cost $0.05y

Total Cost:

`Aluminum + Plastic = Total`

`0.10x + 0.05y = 500`

b.

If y = 6000.

Solve for x

We have:

`0.10x + 0.05y = 500`

Substitute 6000 for y

`0.10x + 0.05* 6000 = 500`

`0.10x + 300= 500`

Collect Like Terms

`0.10x = 500 - 300`

`0.10x = 200`

Solve for x

`x = 200/0.10`

`x = 2000`