Frank, Mary and Seth shared some sweets in the ratio 4:5:7. Seth got 18 more sweets than Frank. Work out the total number of sweets they shared.

The ratio 4:5:7 is a way of comparing the size of the shares received by Frank, Mary and Seth. It helps to pretend that we are sharing the sweets between some equally-sized boxes: each box has the same number of sweets. The first share is worth 4 boxes of sweets, the second is 5 boxes and the third is worth 7 boxes. (It is helpful to draw a box diagram here.)

Firstly, let's match up the order of names to the shares given in the ratio. As the first name, Frank gets the first share, 4 boxes of sweets. As the second name, Mary gets the second share, 5 boxes. Seth gets the third share, worth 7 boxes. (We can label our box diagram to represent this.)

We should use the information from the question, "Seth got 18 more sweets than Frank". We also know how many boxes of sweets this is. Since Seth has 7 boxes and Frank has 4 boxes, Seth has 3 boxes more than Frank (7 - 4 = 3). That means that the extra 18 sweets Seth got are shared between the extra 3 boxes he got. (This can also be added to our diagram.)

Remembering that each box is equally sized, this means we can find out how many sweets go in one box: 18 sweets ÷ 3 boxes = 6 sweets per box. (We can add this to our diagram.)

Now, to work out how many sweets there are in total, we simply need to multiply 6 (sweets per box) by the number of boxes that there are. Frank has 4, Mary has 5, Seth has 7. 4 + 5 + 7 = 16, and so there are 16 boxes of sweets in total. 6 sweets per box * 16 boxes = 96 sweets in total. Therefore, the total number of sweets shared between Frank, Mary and Seth is 108.