Question

The sum of four consecutive multiples of 9 is 378. Find these multiples? [3 MARKS]

Answer 1

Framing the equation: 1 Mark
Steps: 1 Mark
Result: 1 Mark

Let the first number be $9x$

Then, second consecutive number $=9(x+1)$

Third consecutive number $=9(x+2)$,

And, fourth consecutive number $=9(x+3)$

According to question:

$9x+9(x+1)+9(x+2)+9(x+3)=378$

$\Rightarrow 9x+9x+9+9x+18+9x+27=378$

$\Rightarrow 36x+54=378$

$\Rightarrow 36x=378-54$

$\Rightarrow 36x=324$

$\Rightarrow x=\frac{324}{36}=9$

The numbers are 81, 90, 99 and 108.