Dividing in Certain Ratios

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Three men – Alf, Bob and Cliff – have £150 to share between them for a job of work. Being all fair of mind they decide to divide the money in proportion to the work they have done. They decide therefore to share the money in the ratio 4:5:6. They draw up the following table.

Name

Share

£

Alf

4

Bob

5

Cliff

6

Total

15

150

If they only had £15 to share, it would be simple. Alf could have £4, Bob could have £5 and Cliff could have £6. In fact the have £150 to share out and we have to fill out the £ column so that the money is shared in the ratio 4:5:6 and the sum of Alf’s, Bob’s and Cliff’s share is !50. But look! The total in the Share colum is !5 and the total in the £ column is £150! If we just multiply the shares column by 10 we obtain the £ column. The completed table is given below.

Name

Share

£

Alf

4

40

Bob

5

50

Cliff

6

60

Total

15

150

We can always do this – find the scale factor from the shares column to the £ (or whatever is actually being shared out column) then multiply the shares by the scale factor to get the answers.

Example:

Share 180 in the ratio 7:3:2

Share

Quantity

7

105

3

45

2

30

Total

12

180

The scale factor from the share to the quantity column is 15 – worked out from the bottom row – so multiply the share colum by 15 to get the quantity column.

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