Question

A woman has 21 total coins in her pocket, all of which are either dimes or quarters. If the total value of her change is $3.90, how many dimes and how many quarters does she have? Write the number of dimes, then the number of quarters separated by a comma.

Answer 1

The woman has 12 quarters and 9 dimes.

Explanation:

Givens

• The woman have 21 total coins.
• The coins are distributed between dimes ad quarters.
• The total value of her change is $3.90.

With this information we can construct a system of equations, where
`d` is dimes and
`q` is quarters.

`d+q=21`, because there are 21 coins between dimes and quarters.

Now, we know that one dime values 10 cents, and one quarter values 25 cents.

`0.10d+0.25q=3.90`, because the woman has $3.90 in total.

Then, we isolate
`d` in the first expression

`d=21-q`

And we substitute it in the second expression

`0.10d+0.25q=3.90\\0.10(21-q)+0.25q=3.90\\2.1-0.10q+0.25q=3.90\\0.15q=3.90-2.1\\q=(1.80)/(0.15) \\q=12`

Then, we use this value to find the other one

`d=21-q\\d=21-12\\d=9`

Therefore, the woman has 12 quarters and 9 dimes.

Answer 2

Answer with Step-by-step explanation:

Let there be d dimes and q quarters

A woman has 21 total coins in her pocket.

⇒ d+q=21 ------(1)

1 dime=$ 0.1

1 quarter=$ 0.25

The total value of her change is $3.90

⇒ 0.1d+0.25q=3.90

Multiplying both sides by 100,we get

10d+25q=390 --------(2)

(2)-10×(1)

10d+25q-10d-10q=390-210

15q=180

Dividing both sides by 15, we get

q=12

Putting value of q in (1),we get

d=9

Hence, Number of dimes=9

and number of quarters=12

Write the number of dimes, then the number of quarters separated by a comma.

9,12