I was standing in a queue in the village shop near Quizmastershop Towers. It was very odd, but all five customers in front of me were buying two items, as was I.
The first bought Tomato Ketchup and Sugar for £2.70.
The next paid £1.45 for a Croissant and Baked Beans.
A sweet-toothed customer next with Honey and Sugar for £3.55.
The fourth customer's Baked Beans and Tomato Ketchup cost £1.55.
And finally Honey and a Croissant came to £2.85.
Having patiently waited my turn I paid £2.40 for my two items.
But what did I buy?
The method here is to find the price of one of the five items purchased, and then work out the prices of the other four. One way is:
TK + S = 270 and
TK + BB = 155
subtracting gives
S - BB = 115 or
BB = S - 115 (a)
then
H + S = 355
H + C = 285
subtracting gives
S - C = 70 or
C = S - 70 (b)
We now have BB and C in terms of S and we have BB and C in one equation
C + BB = 145
S - 70 + S - 115 = 145
2S - 185 = 145
2S = 145 + 185 = 330
S = 165
So now we know Sugar costs £1.65 and successively putting known values into the equations that we have, we can find out that
Honey costs £1.90
Tomato Ketchup costs £1.05
A Croissant costs 95p
And Baked Beans cost 50p
The only two of these that add up to £2.40 are Honey and Baked Beans