Mathematics, 18.07.2019 18:40 payshencec21

Rufus collected 100 pounds of aluminum cans to recycle. he plans to collect and additional 25 pounds each week. write the equation for the total pounds, p, of aluminum cans after w weeks. what does the slope and y-intercet represent? how long will it take rufus to collect 400 pounds of aluminum cans?

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Answer from: jeffffffff

The equation for the total pounds P, of aluminum cans that can be collected after W weeks is P = 100 + 25W

Number of pounds of aluminum cans to recycle = 100Additional pound of cans to be collected = 25 pounds Number of weeks = W

Therefore, the equation for the total pounds,P, of aluminum cans that can be collected after W weeks will be:

= 100 + (25 × W)

P = 100 + 25W

The slope and y-intercept represent are 25 and 100 respectively.

The number of weeks that'll be taken to collect 400 pounds of aluminum cans will be:

P = 100 + 25W

400 = 100 + 25W

Collect like terms

25W = 400 - 100

25W = 300

W = 300/25

W = 12.

Therefore, Rufus will take 12 weeks to collect 400 pounds of aluminum cans.

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Answer from: puppylove899

Slope represents that the weight of can increased by 25 pounds each week. Y-intercept represents initial weight of cans, i.e., 100 pounds.

The time taken by Rufus to collect 400 pounds of aluminum cans is 12 weeks.

Step-by-step explanation:

It is given that Rufus collected 100 pounds of aluminum cans to recycle. He plans to collect and additional 25 pounds each week.

It means initial weight of cans = 100 pounds

Additional weight of cans = 25 pounds each week

Let W be the number of week.

The equation for the total pounds P of aluminum cans after W weeks is

P=100+25W .... (1)

The slope intercept form of a line is

y=mx+b .... (2)

where, m is slope and b is y-intercept.

From (1) and (2) we get

m=25,b=100

It means slope and y-intercept are 25 and 100 respectively.

Slope represents that the weight of can increased by 25 pounds each week. Y-intercept represents initial weight of cans, i.e., 100 pounds.

We need to find the time taken by Rufus to collect 400 pounds of aluminum cans.

Substitute P =400 in equation (1).

400=100+25W

Subtract 100 from both sides.

400-100=25W

300=25W

Divide both sides by 25.

12=W

Therefore, the time taken by Rufus to collect 400 pounds of aluminum cans is 12 weeks.

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