Linear system help

Question

You have a total of 35 coins, all Nickels ($0.05) and quarters ($0.25) . The total value is $5.75. Write and solve a system of equations to find the number of Nickles and quarters .

Answer 1

x + y = 35

0.05x + 0.25y = 5.75

Answer 2

The first equation comes from the total number of coins which only involves nickels and quarters.

N + Q = 35

The second equation comes from the total value of the nickels and quarters.

.05Q + .25Q = 5.75

You now have a linear system:

N + Q = 35

.05N + .25Q = 5.75

You have the option of solving this system by substitution, elimination, and graphing. I will solve by using elimination. I will multiply all terms in equation 1 by -.05. Creating the following new equation 1:

-.05N - .05Q = -1.75

The new linear system is:

-.05N - .05Q = -1.75

.05N + .25Q = 5.75

Adding both equations together yields the following:

.20Q = 4

Q = 20 (dividing both sides by .20)

Using the original equation 1 we can solve for N.

N + 20 = 35

N = 15 (subtracting 20 from each side of the equation)

To verify we substitute our answers back into both equations (original linear system).

15 + 20 = 35

.05(15) + .25(20) = 5.75 = .75 + 5

Both equations check so the number of coins is 15 nickels and 20 quarters.