Answer:
Gina has 29 nickels and 72 dimes.
Step-by-step explanation:
Each nickel is $0.05, and each dime is $0.10.
If she has 101 total coins, we have:
[tex]nickel + dime = 101[/tex]
All coins worth $8.65, so we have:
[tex]0.05nickel + 0.1 dime = 8.65[/tex]
Multiplying the second equation by 20, and subtracting the result by the first equation, we have:
[tex]20(0.05nickel + 0.1 dime) - nickel - dime = 20*8.65 - 101[/tex]
[tex]1nickel +2 dime - nickel - dime = 173 - 101[/tex]
[tex]dime = 72[/tex]
Then, finding the number of nickels, we have:
[tex]nickel + 72 = 101[/tex]
[tex]nickel = 29[/tex]
So Gina has 29 nickels and 72 dimes.
