Brainbuster

[Indilia]

Jill has enough money to buy either 6 melons and 7 lemons or 8 melons and 4 lemons. Both options leave her with no change. If she bought only lemons how many could she afford? I know the answer is 16 but how is it worked out?

[Toorak]

If you assume that a lemon costs £1 then she has £16 in total. That means that if she buys 4 lemons and 8 melons, melons must cost £1.50 each.

6 melons = £9 + 7 lemons = £7

£9 + £7 = £16

[Toorak]

It would work whatever the cost per unit - melons cost 1.5 times the cost of lemons

[IJKLM]

If you want the algebraic way of doing it, let's say the following:

Price of a melon = M
Price of a lemon = L
Amount of cash = C

C=6M+7L (first equation)
C=8M+4L

6M+7L=8M+4L
Subtract 6M from both sides:

7L=2M+4L
Subtract 4L from both sides:

3L=2M

Substitute back into the first equation:

C=9L+7L

So Jill can buy 16 lemons, with no change.

[fiction-factory]

In cost terms:

8 melons & 4 lemons = 6 melons & 7 lemons
So the trade off is 2 melons= 3 lemons

Continuing the pattern:
6 melons& 7 lemons
= 4 melons & 10 lemons
= 2 melons & 13 lemons
= 0 melons & 16 lemons