I need help with this maths question?

Question

3 cups of coffee and a cake cost £1.90 2 cups of coffee and 2 cakes cost £2.20 how much does one cup of coffee cost? I need to know how you work it out as well. thanks

Im very sorry to people who have already answered but I made a mistake in the question it is actually 3 cups of coffee and 1 cake =1.90 2 cups of coffee and 3 cakes=2.20

Answer 1

Start by calling a cup of coffee 'x' and a cake 'y'.

So, if 3 cups of coffee and one cake cost 1.90, it can be re-written as:
3x+y=1.90
and similarly the second statement can be re-written as
2x+3y=2.20
Now you have two equations which you can solve to find out what x (the price of a cup of coffee is.
In order to do this you have to make the values for y the same in both equations, so you have ti multiply the whole first equation by 3.

So now the equations you have are
3*(3x+y=1.90)
2x+3y=2.20

which is:
9x+3y=5.70
2x+3y=2.20

now subtract the bottom equation from the top one and see what you're left with.(ie 9x-2x, 3y-3y and 5.70-2.20)

this gives you the equation
7x=3.50
That means that 7 cups of coffee cost 3.50
In order to find out what one costs, divide both sides by 7,
7x/7=x and 3.50/7=0.50
So one cup of coffee costs £0.50

I hope this helped

Answer 2

40p

3x + y = 1.90
2x + 3y = 2.20

x is the cups of coffee, so we'll solve for that.
multiply the first equation by -3

-9x -3y = -5.70
2x + 2y = 2.20

Add the two equations together

-7x = -3.50

Divide by -7

x = .50