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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.

2 Answers

3 votes

Answer:

there are 15 dimes and 14 quarters.

Explanation:

User Akif
by
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0 votes

Answer:

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.

User Abdellah OUMGHAR
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