twelveminus wrote:

These types of questions are very common, but more commonly use two variables, e.g., 'A Meat Pie is £2.20, and a Pasty is £1.90. If John spends £23 on meat pies and pasties, how many of each does he buy?'

When the quantities involved are too high to make writing out all the combinations a sensible strategy you could also approach this by taking the amount spent and dividing by the minimum and maximum prices to get an approximate number of items:

£23/£1.90 = 12.1 (round this one down)

£23/£2.20 = 10.45 (round this one up)

N.B. - you don't actually have to get to 12.1 or 10.45, just to determine that its 12.something (but less than 13) and 10.something (but less than 11) and then round appropriatelySo 11 or 12 items altogether.

Start by assuming all of one type of item, and then adjust to get the answer:

11 pasties would be £20.90 - so need to increase spend by £2.10

Each time you replace 1 pastie with a pie the spend increases by 30p

To get to £2.10 you'd need to do this 7 times.

So 7 pies and 11-7 (i.e. 4) pasties

Had the amount of adjustment needed (£2.10) not divided equally by the price difference (30p) you could have moved on to trying the other option of 12 items.