Ratio question: Paul and Luke share some money in the ratio 4:7. Paul gets £12 less than Luke. How much did they have in total?

Need to use bar model.

P/L=4/7 and P=L-12 so

(L-12) / L=4/7 multiply both sides by 7

(7L-84) / L=4 multiply both sides by L

7L-84=4L subtract 4L from both sides

3L-84=0 add 84 to both sides

3L=84 divide both sides by 3

L=28, and since P=L-12

P=16

So they had 28+16 = £44 in total.