SOLUTION: Please help me with this question. A piece of pasture grows at a constant rate every day. 200 sheep will eat up the grass in 100 days. 150 sheep will eat up the grass in 150 days

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Question 337451: Please help me with this question.
A piece of pasture grows at a constant rate every day. 200 sheep will eat up the grass in 100 days. 150 sheep will eat up the grass in 150 days. How many days does it take for 100 sheep to eat up the grass?

Found 2 solutions by stanbon, miampetite:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A piece of pasture grows at a constant rate every day. 200 sheep will eat up the grass in 100 days. 150 sheep will eat up the grass in 150 days. How many days does it take for 100 sheep to eat up the grass?
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You are given 2 pairs of points that relate # of sheep and time to eat the grass: (200,100) and (150,150)
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slope = (150-100)/(150-200) = 50/-50 = -1
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y-intercept:
100 = (-1)(200) + b
100 = -200 + b
b = 300
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Equation:
# of days = -1(# of sheep) + 300
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Then:
D(100_ = -100 + 300
D(100) = 200 (100 sheep will take 200 days to eat the grass)
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Cheers,
Stan H.

Answer by miampetite(1) (Show Source):
You can put this solution on YOUR website!
The answer should be 300 days.
1 sheep eat 1 unit of grass per day.
200 sheep will eat 200 units of grass per day.
200 sheep will eat 200 x 100 = 20000 units of grass in 100 days.
150 sheep will eat 150x150 = 22500 units of grass in 150 days.
Hence in 50 days the grass grew 22500 - 20000 = 2500 units
in 1 day the grass will grow 2500/50 = 50 units
In 100 days, the grass would have grown 50 x 100 = 5000 units.
hence initial grass = 20000 - 5000 = 15000 units
Days taken for 100 sheep to eat up the grass = X.
15000 + 50X = 100X
50X = 15000
X = 300 days.