Let

A denote the quantity of grass per acre when the pasture starts to be used

 

B the quantity of grass eaten by one ox in one week

 

C the quantity of grass that grows on one acre in one week

 

a, b, c the numbers of oxen,

m, n, p the number of acres,

h, j, k the numbers of weeks in the three cases considered, respectively.

 

A, B, and C and c are unknown. The conditions are

 

m(A + hC) = ahB

n(A + jC) = bjB

p(A + kC) =ckB

a system of equations for the three unknowns A/B, C/B, c . . .

With numerical datea for m, n, p, h, j, k, a, and b (respectively 3 1/3, 10, 24, 4, 9, 18, 12, and 21) the result is 36.

 

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(10/3)(A + 4C) = (12)(4)B

10(A + 9C) = 21(9)B

24(A + 18C) = c(18)B

Let x = A/B, y = C/B

 

(10/3)(x + 4y) = (12)(4)

10(x + 9y) = (21)(9)

(24(x + 18y) = 18c