Grass Consumption by Oxen
Molly McKee
If 6 acres of grass, together with what grows on the 6 acres during the time of grazing, keep 16 oxen for 12 weeks, and 9 acres keep 26 oxen 9 weeks, how many oxen will 15 acres keep 10 weeks, the grass growing uniformly all the time?
The Problem
g = the amount of grass per acre
h = new grass, per acre, per week
k = the amount of grass eaten by each ox
Equation 1:
6g + (6)(12)h = (16)(12)k
6g + 72h = 192k
Equation 2:
9g + (9)(9)h = (26)(9)k
9g + 81h = 234k
Equation 3:
15g + (15)(10)h = (X)(10)k
15g + 150h = 10kX
Solve for X:
Solve for k:
Solve for g in terms of h:
Therefore, g = 4h
Solve for h in terms of k:
6(4h) + 72h = 192k 9(4h) + 81h = 234k
96h = 192k 117h = 234k
h = 2k h = 2k
Therefore, g = 4h = 8k
Solve for X:
15(8k) + 150(2k) = 10kX
120k + 300k = 10kX
12 + 30 = X
42 = X
15 acres will keep 42 oxen for 10 weeks.
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