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

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.