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Rufus collected 100 pounds of aluminum cans ro recycle. He plans to collect an additional 25 pounds each week. His brother decides he wants to start collecting cans. He does not have sny to begin with, but he collects 35 pounds per week. How long before he catches up to Rufus?

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TaeKwonDoIsDead

Answer:

10 weeks

Step-by-step explanation:

We can create 2 equations for each person and equate them to find the time.

Rufus already collected 100, so that's fixed. 25 pounds per week means 25x (let x be number of weeks). So Rufus' equation is:

100 + 25x

Brother doesn't have anything yet, so no fixed amount. But he collects 35 pounds per week (x amount of weeks). So his equation would be:

35x

For them to equate (brother to catch-up), we can equate both equations and solve for x (number of weeks required):

[tex]100+25x=35x\\100=35x-25x\\100=10x\\x=\frac{100}{10}\\x=10[/tex]

So, his brother would need 10 weeks to catch up to Rufus

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