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Answer:
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
[tex]P=100+25W[/tex] .... (1)
The slope intercept form of a line is
[tex]y=mx+b[/tex] .... (2)
where, m is slope and b is y-intercept.
From (1) and (2) we get
[tex]m=25,b=100[/tex]
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).
[tex]400=100+25W[/tex]
Subtract 100 from both sides.
[tex]400-100=25W[/tex]
[tex]300=25W[/tex]
Divide both sides by 25.
[tex]12=W[/tex]
Therefore, the time taken by Rufus to collect 400 pounds of aluminum cans is 12 weeks.
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 = 100
- Additional 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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