A piggy bank contains quarters and dimes. There are 30 coins in the jar, and the total value is $6.30. How many quarters and dimes are in the piggy bank?

Answer 1

I will use q for quarters and d for dimes. If I have a total of 30 coins, that means that the amount of quarters PLUS the amount of dimes is equal to 30. Meaning, q + d = 30. (this is your first equation).

Now, the value of a quarter is $0.25 and the value of a dime is $0.10. Therefore, when you have, let's say 5 quarters, you have $1.25 because 0.25 x 5 = 1.25. Same principle applies to the dimes. If I have, let's say 5 dimes, I have $0.50 because because 0.10 x 5 = 0.5.

By this logic, if we multiply q x $0.25, we get the amount of money we have in quarters, and if we multiply d x $0.10, we get the amount of money we have in dimes. Therefore, 0.25q + 0.10d = total amount of money you have.

According to the problem, the total amount of money you have is $6.30. That means that 0.25q + 0.10d = 6.30 (this is your second equation).

Bringing it all together:

q + d = 30

0.25q + 0.10d = 6.30

You now have to solve for q (or d) on your first equation and substitute it into your second equation. (I will solve for q).

q = 30 - d

0.25 (30 - d) + 0.10d = 6.30

Now you solve like you would any other equation:

7.25 - 0.25d +0.10d = 6.30

7.25 - 0.15d = 6.30

- 0.15d = 6.30 - 7.25

- 0.15d = -1.2

now divide by -0.15 on both sides

d = 8 (I have 8 dimes)

How many quarters do you have?

q = 30 - d

q = 30 - 8

q = 22 (I have 22 quarters)

Answer 2

Q+D = 30

25Q + 10D = 630

25Q + 25D = 750

subtract them to get

15D = 120

D = 40/5 = 8 dimes

Q = 30-8 = 22 quarters

25(22) + 10(8) = 550 + 80 = 630