Question

A coin purse contains d dimes and q quarters. There are 35 coins in the purse, and the total value of the coins is $5.60. Create the system of linear equations and use it to find how many dimes and quarters are in the purse.

Answer 1

14 dimes, 21 quarters

Explanation:

Represent dimes with d and quarters with q.

So: 35 coins means

`d + q = 35`

1 dime = $0.10 and 1 quarter = $0.25. So, a value of $5.60 means

`0.10d + 0.25q = 5.60`

So, the system of equations is:

`d + q = 35`

`0.10d + 0.25q = 5.60`

Make d the subject in
`d + q = 35`

`d = 35 - q`

Substitute 35 - q for d in
`0.10d + 0.25q = 5.60`

`0.10d + 0.25(35 - q) = 5.60`

Open bracket

`0.10d + 8.75 - 0.25q = 5.60`

Collect Like Terms

`0.10d - 0.25q = 5.60 - 8.75`

`-0.15q = -3.15`

Solve for q

`q = (-3.15)/(-0.15)`

`q = 21`

Substitute 21 for q in
`d = 35 - q`

`d = 35 - 21`

`d = 14`