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Solve using Algebra. Say that 70 cows take 24 days to eat all the grass in a pas

ID: 3090391 • Letter: S

Question

Solve using Algebra.

Say that 70 cows take 24 days to eat all the grass in a pasture.The same pasture sustains 30 cows for 60 days. how many cows wouldtake 96 days to eat all the grass? Assume that all grass growa at the same rate and that all thecows eat the grass at the same rate Solve using Algebra.

Say that 70 cows take 24 days to eat all the grass in a pasture.The same pasture sustains 30 cows for 60 days. how many cows wouldtake 96 days to eat all the grass? Assume that all grass growa at the same rate and that all thecows eat the grass at the same rate

Explanation / Answer

a = length of the grass at first
b = rate at which grass grows
c = rate at which a cow eats grass
d = number of cows that would take 96 days to eat all the grass

70 x 24c = a + 24b, so 1680c = a + 24b
30 x 60c = a + 60b, so 1800c = a + 60b
which means 120c = 36b

70 x 24c = a + 24b, so 1680c = a + 24b
d x 96c = a + 96b, so   96cd = a + 96b
so 96cd -1680c = 72b
                      
As 120c = 36b, and 96cd-1680c = 72b, then 2(120c) = 96cd-1680c.
So 240c = 96cd-1680c. Factor out c, and we’re left with96d-1680 = 240.

Which means 96d = 1920, so d (the number of cows) equals 20