Question

Sam the scout is going on a camp out with his boy-scout troop. There are large tents that sleep 6 boys and small tents that sleep 4 boys. The ratio of large tents to small tents is 8 to 5. There are exactly enough tents to sleep 816 boys. How many tents of each size are there?

Answer 1

There are 96 large tents and 60 small tents

Explanation:

Here, we want to calculate the number of tents of each sizes there

Let the number of 6-boys tent be s and the number of 4-boys tent be f

6s + 4f = 816 ••••••(i)

Ratio of large to small ( ratio of s to f)

8:5 = s/f

8/5 = s/f

8f = 5s

f = 5s/8 ••••(ii)

Substitute ii into i

6s + 4(5s/8) = 816

6s + 5s/2 = 816

Multiply through by 2

12s + 5s = 1,632

17s = 1632

s = 1632/17

s = 96

f = 5s/8

f = (5 * 96)/8 = 60