Question

the ratio of the ages of four members of a family is 9 : 8 : 3 : 2. the average of the family is 22 years. what is the age of the eldest person in the family? a. 12 years b. 6 years c. 36years d. 32years

Answer 1

(c) 36 years

Explanation:

given the ratio of the 4 members of a family is

9 : 8 : 3 : 2 = 9n : 8n : 3n : 2n ( n is a multiplier )

with 9n being the oldest

the average is calculated as

average =
`(sum)/(count)` =
`(9n+8n+3n+2n)/(4)` =
`(22n)/(4)`

given the average age of the four members is 22 , then

`(22n)/(4)` = 22 ( multiply both sides by 4 )

22n = 4 × 22 = 88 ( divide both sides by 22 )

n = 4

then eldest = 9n = 9 × 4 = 36 years