Question

Dustin has only nickels and quarters in his piggy bank. He was 49 total for combined value of $8.85. How many of each type of coin does he have

Answer 1

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.