Respuesta :
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:
[tex]q+d=29...(1)[/tex]
[tex]q=29-d...(1)[/tex]
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:
[tex]0.25q+0.10d=5...(2)[/tex]
Upon substituting equation (1) in equation (2), we will get:
[tex]0.25(29-d)+0.10d=5[/tex]
[tex]7.25-0.25d+0.10d=5[/tex]
[tex]7.25-0.15d=5[/tex]
[tex]7.25-7.25-0.15d=5-7.25[/tex]
[tex]-0.15d=-2.25[/tex]
[tex]d=\frac{-2.25}{-0.15}[/tex]
[tex]d=15[/tex]
Therefore, there are 15 dimes in the collection.
Upon substituting [tex]d=15[/tex] in equation (1), we will get:
[tex]q=29-d\Rightarrow 29-15=14[/tex]
Therefore, there are 14 quarters in the collection.
