Question

In a group of 100 adults, 70 say they are most likely to do spring houseclean-ing in March, April, or May. Of these 70, the number who clean in April is 14 more than the total number who clean in March and May. The total number who clean in April and May is 2 more than three times the number who clean in March.

Answer 1

Adults that clean in March = 18

Adults that clean in April = 48

Adults that clean in May = 4

Explanation:

Adults that clean in the months of March, April and May = 70

Let a represent March, b represent April and c represent May.

Therefore, a + b + c = 70 (i)

From the question, the number of adults that clean in April is 14 more than number of the adults cleaning in months of March and May combined.

b - ( a + c) = 14 (ii)

also, the total number who clean in April and May is 2 more than three times the number who clean in March.

b + c - 3a = 2 (iii)

From (i), a + c = 70 - b (iv)

Substituting (iv) into (ii), b - ( 70 - b) = 14

b -70 + b = 14

2b = 84, b =48

Therefore a + c = 70 - 48

a + c = 22; c = 22 - a (v)

Substituting (v) and b = 48 into (iii)

48 + 22 - a -3a = 2

4a = 72, a = 18

Therefore, c = 22 - 18

c = 4