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