Let's use the variables N and Q for the number of nickels and the number of quarters.
We know there are 49 total coins, so we can write the following equation:
N + Q = 49
We can solve this equation for one variable which will help in the next step. Let's solve for N:
N = 49 - Q
Next, we know that nickels are worth $0.05 and quarters are worth $0.25. We can use these values along with the total value of $8.85 to create another equation.
0.05N + 0.25Q = 8.85
Now we can use substitution to solve our system out equations. We solved the first equation for N, so we can plug 49 - Q in for N.
0.05(49-Q) + 0.25Q = 8.85
Distribute and combine like terms.
2.45 - 0.05Q + 0.25Q = 8.85
2.45 + 0.2Q = 8.85
0.2Q = 6.4
Q = 32
Plug 32 in for Q in N + Q = 49 to find the number of nickels.
N + 32 = 49
N = 17
Dustin has 32 quarters and 17 nickels.
