Expert: Bobby Soltani - 12/18/2005

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

Answer
Hi Tiffany,

This is one of the problems where you have two unknowns, so you need two equations to solve them.  Let d be the number of dimes and q be the number of quarters.  We know that there are 30 coins, so

d + q = 30

Also, we know that the total is worth $4.20.  Since a dime is worth $0.10, and a quarter is worth $0.25, we can write

0.10d + 0.25q = 4.20

Now we have our two equations.

Solve the first one for d by subtracting q from both sides.

d = 30 - q

Now substitute 30 - q in for d in the second equation.

0.10(30 - q) + 0.25q = 4.20

Now, we just have one equation in q, so we can solve it.

3 - 0.10q + 0.25q = 4.20
3 + 0.15q = 4.20
0.15q = 1.20
q = 8

now, plug 8 in for q in the first question.

d + 8 = 30

d = 22

So, there are 22 dimes and 8 quarters.  Let me know if you have any questions.

Bobby