Answer: Dimes= 20, Nickels= 15
Explanation:
Since we are looking for the amount of coins, we can use system of equations to solve for the amount of coins.
Equation 1:
0.1x+0.05y=2.75
This equation comes from the total cost. x stands for dimes and y stands for nickels. 0.1 is the worth of a dime and 0.05 is the worth of a nickel.
Equation 2:
x=2y-10
This equation comes from 10 less than twice the number of nickels.
We can use substitution to find x and y.
0.1(2y-10)+0.05y=2.75
0.2y-1+0.05y=2.75
0.25y-1=2.75
0.25y=3.75
y=15
There are 15 nickels.
Now that we have y, we can plug it back into the equation to find x.
x=2(15)-10
x=30-10
x=20
There are 20 dimes.