Question

Three numbers are in the ratio 4:3:2 and their average is 63.

(1) Calculate the sum of the three numbers. (1) find all the three numbers.
(11) by how much is the smaller number less than the bigger number?​

Answer 1

see explanation

Explanation:

the average is calculated as

average =
`(sum)/(count)`

(i) the 3 numbers are in the ratio 4 : 3 : 2 = 4x : 3x : 2x ( x is a multiplier )

sum of 3 numbers = 4x + 3x + 2x = 9x

then

`(sum)/(3)` = 63 ( multiply both sides by 3 )

sum = 3 × 63 = 189

9x = 189 ( divide both sides by 9 )

x = 21

then

4x = 4× 21 = 84

3x = 3 × 21 = 63

2x = 2 × 21 = 42

the sum of the 3 numbers is 189 and

the 3 numbers are 84, 63 , 42

(ii)

largest number = 84 and smallest number = 42

smallest number is 84 - 42 = 42 less than the biggest number