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7th Grade Challenging Math

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7-45)   Answer

          5 days

Solution:

The amount of grass that 10 sheep eat in 20 days = original amount of grass + new growth in 20 days
The amount of grass that 15 sheep eat in 10 days = original amount of grass + new growth in 10 days

Assume the amount of grass one sheep eats in one day is 1.  Therefore,
The amount of grass 10 sheep eat in 20 days = 1 x 10 x 20 = 200
The amount of grass 15 sheep eat in 10 days = 1 x 15 x 10 = 150

The amount of grass that grows in 10 days is 200-150 = 50
The amount of grass that grows in one day is 50/10 =
5, which can feed 5 sheep for one day;
Therefore the original amount of grass is 200 - 5 X 20 =100

Since new grass grows in one day can feed 5 sheep, the original grass only needs to feed 20 sheep. (25 - 5 = 20)
Therefore, 25 sheep can feed on the land for 100/(25 -
5) = 5 days

 

 

 

 

 
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