Question

I buy x choc ices and y orange ices and spend $2.30. I buy ten ices altogether . the choc ices cost $0.30 each and the orange ices cost $0.20 each. How many of each do I buy?

I understand how to get to two equations from the problem. All the equations thatI tried are not working out. Please help me out!

Answer 1

`3` chocolate ices and `7` orange ices

Explanation:

So the two equations that you are going to make are as follows. The first is about amount, the second is about cost .

Since you bought 10 total, this is the first equation:
`x + y = 10`

Since chocolate ice costs `"30 cents"` (or `30/100` of a dollar) and orange ice costs `"20 cents"` (or `20/100` of a dollar) we can make this equation:

`0.30x + 0.20y = 2.30`

I'm actually going to multiply that whole equation by `10` to move the decimal points one places and make it easier to solve:

`3x + 2y = 23`

Now rearrange the first equation to substitute into the second:
`x + y = 10`
`x = 10 - y`

Now substitute:
`3x + 2y = 23`
`3(10-y) + 2y = 23`
`30 - 3y + 2y = 23`
`30 - y = 23`
`-y = - 7`
`y = 7`

You bought `7` orange ices.

Now put the value of `y` into an equation to solve for `x`
`x = 10 - y`
`x = 10 - 7`
`x = 3`

You bought `3` chocolate ices.