Question

If the sum of three consecutive multiples of 9 is 108, then find the average of multiples.$\left[4Marks\right]$

Answer 1

If x is a multiple of 9, then next multiple is x + 9

The next to this is x + 9 + 9 = x + 18

So three consecutive multiples of 9 are x, x + 9, x + 18$\left[1Mark\right]$

x + (x + 9) + (x + 18) = 108

3x + 27 = 108

x = $\frac{108-27}{3}$ = $\frac{81}{3}$ = 27$\left[1Mark\right]$
So, first multiple is 27
Second multiple is 27 + 9 = 36
Third multiple is 27 + 18 = 45.$\left[1Mark\right]$
Average of multiples = $\frac{27+36+45}{3}$
= 36$\left[1Mark\right]$