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castortr0y [4]
3 years ago
14

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 th

ere in the collection.
Mathematics
1 answer:
Feliz [49]3 years ago
4 0

Answer:

15 dimes and 14 quarters.

Step-by-step 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=\frac{-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.

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