Question

Rufus collected 100 pounds of aluminum cans to recycle. He plans to collect an additional 25 pounds each week. Write and graph the equation for the total pounds, P, of aluminum cans after w weeks. What does the slope and y-intercept represent? How long will it take Rufus to collect 400 pounds of cans?

Answer 1

Step-by-step explanation:

Given that Rufus collected 100 pounds of aluminium cans. He plans to collect an additional 25 pounds each week.

The equation that describes the total pounds of aluminium cans after w weeks is:

`P=100+25w`

The slope is 25, the additional cans he plans to collect each week

and the y-intercept is 100, the initial amount of cans he had collected.

The graph of the equation is displayed below

To know how long it will take Rufus to collect 400 pounds of cans, substitute P = 400 into the equation, and solve for w

Since

P = 100 + 25w

400 = 100 + 25w

Subtract 100 from both sides of the equation

400 - 100 = 100 + 25w - 100

300 = 25w

Divide both sides by 25

300/25 = 25w/25

w = 12

Therefore, it will take Rufus 12 weeks to collecct 400 pounds of cans.