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

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?
---------------
You are given 2 pairs of points that relate # of sheep and time to eat the grass: (200,100) and (150,150)
---
slope = (150-100)/(150-200) = 50/-50 = -1
---
y-intercept:
100 = (-1)(200) + b
100 = -200 + b
b = 300
------------------
Equation:
# of days = -1(# of sheep) + 300
---
Then:
D(100_ = -100 + 300
D(100) = 200 (100 sheep will take 200 days to eat the grass)
==============
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.
RELATED QUESTIONS
If a sheep and cow and eat a pile of grass in 30 days and the same sheep and goat can... (answered by josmiceli)
The hundred-handed monster Briareus was hungry and attacked a flock of 98 sheep. He... (answered by Solver92311)
The hundred-handed monster Briareus was hungry and attacked a flock of 98 sheep. He... (answered by ikleyn)
The hundred-handed monster Briareus was hungry and attacked a flock of 98 sheep. He... (answered by ikleyn,math_tutor2020)
Please help me with this every answer I have tried is wrong. A bacteria culture starts (answered by robertb)
Question 204841: Jack and Bob are farmers. Jack grows apples, Bob grows oranges. On May... (answered by stanbon)
5 sheep ate 150kg of grass in 15 days how many days will 9 sheep eat 90kg of... (answered by Theo,greenestamps,ikleyn)
A goat and a sheep can eat all the grass on a field in 90 days. A sheep and a cow can eat (answered by ankor@dixie-net.com)
Please help me with this question~ A car travels at a constant rate for 3 hours. The... (answered by )