How many of each of these coins does she have?

Question

At the end of her shift a cashier has a total of $7.10 in dimes and quarters. There are 8 more dimes than quarters. How many of each of these coins does she have?

Answer 1

Hi Anet,

Let's create an equation and solve it to find the numbers of dimes and quarters.

We can represent the number of dimes with the variable, d, and the number of quarters with the variable, q .

Since the total value of both coins is $7.10 and each dime is worth 10 cents and each quarter is worth 25 cents, we can write the following equation to show this total: 10d + 25q = 710

Since "there are 8 more dimes than quarters", we can write: d = q + 8

Now we can substitute this expression for d into the first equation and solve for q:

10d + 25q = 710

10 ( q + 8) + 25q = 710

Now use the distributive property, combine like terms, and use inverse operations to solve:

10q + 80 + 25q = 710

35q + 80 = 710

35q + 80 - 80 = 710 - 80

35q = 630

35q/35 = 6300/35

q = 18

She will have 18 quarters.

To find the number of dimes, add 8 to the number of quarters:

d = q + 8

d = 18 + 8

d = 26

She will have 26 quarters.