Answer:
Sara has 25 dimes in her collection.
Step-by-step explanation:
A quarter is 1/4 or 0.25 of a dollar, and a dime is 1/10 or 0.1 of a dollar.
Let [tex]q[/tex] represent the number of quarters Sara has, and [tex]d[/tex] the number of dimes she has. Then we know that:
[tex]q+d=35.[/tex]
And since the total worth of these coins is $5, we have:
[tex]0.25q+0.1d=5.[/tex]
Thus we have two equations and two unknowns:
- [tex]q+d=35.[/tex]
- [tex]0.25q+0.1d=5.[/tex]
From equation 1 we solve for [tex]q[/tex] and get
[tex]q=35-d[/tex]
and put this value into equation 2 and we get:
[tex]0.25(35-d)+0.1d=5.[/tex]
Solve for d we get:
[tex]\boxed{d=25}[/tex]
Therefore there are 25 dimes in Sara's collection.
