9 spoons and 12 knives cost £82.80
work out the cost of 1 knife
In working ,let k be the cost and s be the cost of the spoon
k = 3s (Using the fact that a knife is 3 times the cost of a spoon)
12k + 9s = 82.80
Now, you can substitute the first expression into the second one to get everything in terms of s and then once you have s, you can easily find k.
Think of x being the cost of a knife and y being the cost of a spoon.
x = 3y would show that a knife cost 3 times what a spoon does.
We know from the info that 12 knives and 9 spoons = 82.80. It could be written as 12x + 9y = 82.80
Substitute 3y from our formula into the equation for x.
12(3y) + 9y = 82.80 becomes 36y + 9y + 82.80 which becomes 45y = 82.80, then divide both sides by 45 to solve for y and you get 1.84
Going back to our original equation, x = 3y, we can substitute 1.84 for y and find that x = 5.52.
So we find a knife cost £5.52