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!

1 Answer
CountryGirl
Mar 22, 2018

#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.

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