Millie, Josh and Libby receive a bonus at work. They are paid in the ratio of 2 : 3 : 4. Josh's share is £105. What was the total amount of the bonus before they shared it?

We let x the portion that each of them received. This is a ratio and proportion problem. We solve as follows:

2x + 3x + 4x = Total bonus

Josh share:

105 = 3x

x = 35

Therefore,

2x + 3x + 4x = Total bonus

2 (35) + 3 (35) + 4 (35) = 315