Question

I need help with this crazy Algebra 1a problem!

You have 14 coins in your pocket that are either quarters or nickels. The total value of the coins is $2.50.
A. Write a system of two equations that represents this situation. Let q represent the number of quarters and n represent the number of nickels.
B. Solve each equation for q.
D. What is the solution to the system?
E. Verify that the answer to part D is correct using the answer to part A.
F. How many of each coin are there?

Answer 1

See below.

Explanation:

A. First equation is

q + n = 14

then we have

0.25q + 0.05n = 2.5

Multiply last equation by -20

-5q - n = -50 Now add this to the first equation

-4q + 0 = -36

B. q = -36/-4 = 9.

D Substitute for q in the first equation

9 + n = 14

n = 14 - 9 = 5.

So the solution to the system is q = 9, n = 5.

E Verify this solution by substituting in the second equation:

0.25(9) + 0.05(5)

= 2.25 + 0.25 = 2.50.

- verified.

F. 9 quarters and 5 nickels.