A change machine changes dollar bills into quarters and nickels. lf you receive 12 coins after inserting a dollar bill, how many nickels did you receive?

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Answer 1 · 2016-12-04T14:46:36

$10$ $10$

If we write $n$ $n$ for the number of nickels (5c) and $q$ $q$ for the number of quarters (25c), then we have two simultaneous equations:

$100 = 25 q + 5 n$ $100 = 25q+5n$

$12 = q + n$ $12 = q+n$

Dividing both sides of the first equation by $5$ $5$ we get:

$20 = 5 q + n$ $20 = 5q+n$

Multiplying both sides of the second equation by $5$ $5$ we get:

$60 = 5 q + 5 n$ $60 = 5q+5n$

Subtracting the previous equation, we find:

$40 = 4 n$ $40 = 4n$

Dividing both sides by $4$ $4$ and transposing, we find:

$n = 10$ $n = 10$

So there were $10$ $10$ nickels, making $50$ $50$ c and $2$ $2$ quarters, making the other $50$ $50$ c.