Question

Gavyn and Alex win some money and share it in the ratio 3:2. Gavyn gets £27. How much did they win in total?

Answer 1

27÷3=9
9 is the original number.
9×2=18

the answer is 18.
if you wanted to check your work, 27:18 simplifies down to 3:2.

Answer 2

`3:2=(3)/(2)\\\\\£27-Gavyn's\ win\\\£w-Alex's\ win\\\\\text{The  equation}\\\\(\£27)/(\£w)=(3)/(2)\qquad\text{cross multiply}\\\\3\£w=(2)(\£27)\\\\3\£w=\£54\qquad\text{divide both sides by 3}\\\\\£w=\£18\\\\Total\ win:\ \boxed{\£27+\£18=\£45}`