Answer:
64 dimes and 34 quarters.
Step-by-step explanation:
Let d represent the amount of dimes and q represent the amount of quarter Julie has.
She has in total 98 coins. Therefore:
[tex]d+q=98[/tex]
Each dime is worth 0.10 and each quarter is worth 0.25. Together, they are worth in total $14.90. Therefore:
[tex]0.1d+0.25q=14.90[/tex]
We have a system of equations. We can solve this using substitution.
First, we can multiply the second equation by 100 to simplify. So:
[tex]10d+25q=1490[/tex]
From the first equation, we can subtract q from both sides:
[tex]d=98-q[/tex]
Substitute this into the second equation:
[tex]10(98-q)+25q=1490[/tex]
Distribute:
[tex]980-10q+25q=1490[/tex]
Combine like term:
[tex]15q+980=1490[/tex]
Subtract:
[tex]15q=510[/tex]
Therefore:
[tex]q=34[/tex]
So, Julie has 34 quarters.
Returning to our first equation:
[tex]d+q=98[/tex]
Substitute:
[tex]d+34=98[/tex]
Therefore:
[tex]d=64[/tex]
Thus, Julie has 64 dimes and 34 quarters.
