Question

Cindy, Hao and Raymond have some books. Cindy has three times as many books as Hao and Raymond has half as many books as Hao. Between the three of them, the mean number of books that each person owns is 15. How many books does each person own?

Answer 1

`Cindy = 30`

`Hao= 10`

`Raymond = 5`

Explanation:

Given

Represent each withe first letter of their name;

So:

`C = 3H`

`R = (1)/(2)H`

`(C + R + H)/(3) = 15` --- the average of books

Required

The number of book each has

Substitute
`C = 3H`,
`R = (1)/(2)H` in
`(C + R + H)/(3) = 15`

`(3H + (1)/(2)H + H)/(3) = 15`

Multiply both sides by 3

`3 * (3H + (1)/(2)H + H)/(3) = 15 * 3`

`3H + (1)/(2)H + H = 45`

Take LCM and solve

`(6H + H + 2H)/(2)= 45`

`(9H)/(2)= 45`

Multiply both sides by 2/9

`(2)/(9) * (9H)/(2)= 45 * (2)/(9)`

`H= 45 * (2)/(9)`

`H= 5 * 2`

`H= 10`

`C = 3H`

`C = 3 * 10`

`C = 30`

`R = (1)/(2)H`

`R = (1)/(2) * 10`

`R = 5`