Question

A collection of dimes and quarters has a total value of five dollars and contains 29 coins. How much of each kind of coin are there in the collection.

Answer 1

there are 15 dimes and 14 quarters.

Explanation:

Answer 2

15 dimes and 14 quarters.

Explanation:

Let q represent number of quarters and d represent number of dimes.

We have been given that a collection of dimes and quarters contains 29 coins. We can represent this information in an equation as:

`q+d=29...(1)`

`q=29-d...(1)`

We know each dime is worth $0.10 and each quarter is worth $0.25.

We are also told that the total value of coins is $5. We can represent this information in an equation as:

`0.25q+0.10d=5...(2)`

Upon substituting equation (1) in equation (2), we will get:

`0.25(29-d)+0.10d=5`

`7.25-0.25d+0.10d=5`

`7.25-0.15d=5`

`7.25-7.25-0.15d=5-7.25`

`-0.15d=-2.25`

`d=(-2.25)/(-0.15)`

`d=15`

Therefore, there are 15 dimes in the collection.

Upon substituting
`d=15` in equation (1), we will get:

`q=29-d\Rightarrow 29-15=14`

Therefore, there are 14 quarters in the collection.