SOLUTION: 5 sheep ate 150kg of grass in 15 days how many days will 9 sheep eat 90kg of grass

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Question 1143938: 5 sheep ate 150kg of grass in 15 days how many days will 9 sheep eat 90kg of grass
Found 3 solutions by Theo, greenestamps, ikleyn:
Answer by Theo(13342) About Me  (Show Source):
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5 sheep ate 150 kg of grass in 15 days.
general formula is n * r * t = q
n is the number of sheep
r is the rate that each sheep eats grass
t is the time
q is quantity of grass eaten
when n = 5 and q = 150 kilograms and t = 15 days, the formula becomes:
5 * r * 15 = 150
solve for r to get r = 150 / 75 = 2.
the rate that each sheep eats grass is 2 kilograms per day.
when n = 9 and r = 2 and q = 90 kilograms, the formula becomes:
9 * 2 * t = 90
solve for t to get t = 90 / 18 = 5
9 sheep will eat 90 kilograms in 5 days.


Answer by greenestamps(13200) About Me  (Show Source):
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There are many different ways to solve a problem like this. The other tutor showed one good way using an algebraic formula for the number of kg eaten in terms of the number of sheep, the number of days, and the rate of eating.

Here is another method that many students like to use.

Start with the given information on number of sheep, number of days, and number of kg of grass, then change two of the three numbers at a time in a logical way to end up with 9 sheep and 90kg of grass.

Here is how the solution might go (there are many other different possible paths!):

Start: 5 sheep; 15 days; 150kg of grass

(1) Multiply the number of sheep by 9/5 to get the required 9 sheep; keep the number of days the same. 9/5 as many sheep and the same number of days means 9/5 as many kg of grass:

9 sheep; 15 days; 270kg of grass

(2) Divide the number of kg of grass by 3 to get the required 90kg; of course keep the required 9 sheep. One-third as many kg of grass and the same number of sheep means one-third as many days:

9 sheep, 5 days, 90kg of grass

ANSWER: 5 days for 9 sheep to eat 90kg of grass

Answer by ikleyn(52800) About Me  (Show Source):
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.
If 5 sheep eat 150 kg of grass in 15 days (! GIVEN !), then one sheep eats  150%2F%285%2A15%29 = 150%2F75 = 2 kg of grass per day.


9 sheep in "x" days will eat  2*9*x kilograms of grass, which gives you an equation to find the unknown number of days


    2*9*x = 90  kilograms of grass.


From the equation,  x = 90%2F%282%2A9%29 = 10%2F2 = 5  days.    ANSWER