Question

A recycling center pays 2 cents per aluminum can and 5 cents per glass bottle. The equation 2x+5y=100 describes the number of cans x and bottles y that you need to earn $1.00. What is the value of each intercept, and what does each represent?

Answer 1

Answer x=50

y=20

Explanation:

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Answer 2

The x-intercept is 50 and it means to earn $1 using ONLY aluminum cans, you would have to collect 50 of them.

The y-intercept is 20 and it means to earn $1 using ONLY glass bottles, you would have to collect 20 of them.

Explanation:

To find x intercept, we set y = 0.

To find y intercept, we set x = 0.

x-intercept:

`2x+5y=100\\2x+5(0)=100\\2x=100\\x=50`

The x-intercept is 50 and it means to earn $1 using ONLY aluminum cans, you would have to collect 50 of them.

y-intercept:

`2x+5y=100\\2(0)+5y=100\\5y=100\\y=20`

The y-intercept is 20 and it means to earn $1 using ONLY glass bottles, you would have to collect 20 of them.