A vending machine that takes only dimes and quarters contains 30 coins, with a total value of $4.20. How many of each coin are there?

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Answer 1 · 2018-03-06T21:54:12

There were #22# Dimes and #8# Quarters

#d+q=30# (total coins)

#10d+25q=420# (total cents)

So now we just solve the two equations for each other using substitution.

#d=30-q#

#10(30-q)+25q=420#

#300-10q+25q=420#

#300+15q=40#

#15q=120#

#q=8#

If we plug that back in, we find that #d=22#

Hope that helps!
~Chandler Dowd