Jenny and Kath hire the canal boat for 14 days. They share the hire cost of £1785.00 in the ratio 2:3. Work out the smaller share.

£714.00

Step-by-step explanation:

The first step is to set up expresssions for the two shares:

Let  x = the amount of one share.  The other share is 1785 - x.  You don't have to worry about which is smaller--that part will work out automatically!

The two shares are in the ratio of 2:3, so set up the proportion

Again, you don't have to worry--you could set up the proportion "upside down" and everything will work out in the end.

Solve the proportion for  x  by "cross multiplying" -- use the Means-Extremes Property of proportions.

So one share is £714£ and the other is £1785 - £714 = £1071.

The smaller share is £714.