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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.

Respuesta :

MrRoyal

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. [tex]0.10x + 0.05y = 500[/tex]

b. 2000 cans

Step-by-step explanation:

We have the following:

[tex]Cost = \$0.10[/tex] per aluminum

[tex]Cost = \$0.05[/tex] per plastic bottle

[tex]Total = \$500[/tex]

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:

[tex]Aluminum + Plastic = Total[/tex]

[tex]0.10x + 0.05y = 500[/tex]

b.

If y = 6000.

Solve for x

We have:

[tex]0.10x + 0.05y = 500[/tex]

Substitute 6000 for y

[tex]0.10x + 0.05* 6000 = 500[/tex]

[tex]0.10x + 300= 500[/tex]

Collect Like Terms

[tex]0.10x = 500 - 300[/tex]

[tex]0.10x = 200[/tex]

Solve for x

[tex]x = 200/0.10[/tex]

[tex]x = 2000[/tex]