2420.21 – Horses and Oats

A farmer is going to the state fair to enter his horses in the long face competition. How much food should he take? Nine bags of oats feed his 8 horses for 7 days. He is taking 5 horses to the contest for a total of 4 days. Will 6 bags of oats be enough?

Solution

Since 9 bags last 8 horses 7 days, 6 bags will last 8 horses 23\dfrac{2}{3} as long, that is for 23×7=143=223\dfrac{2}{3} \times 7 = \dfrac{14}{3} = 2 \dfrac{2}{3} days. By the same kind of thinking, 6 bags will last 5 horses 85\dfrac{8}{5} times longer, that is, for 85×143=11215=7715\dfrac{8}{5} \times \dfrac{14}{3} = \dfrac{112}{15} = 7 \dfrac{7}{15} days (roughly a week).

More than enough! So 66 bags of oats will be sufficient. He could get by with fewer bags. (Ha, but how many fewer?)