Question

Margie has 5 times as many nickels as quarters. She has a total of $2.00.

a. Write a system of equations to represent the situation. Let n represent the number of nickels and q represent the number of quarters.
b. Solve the system you wrote in part (a). Show your work.
c. Interpret your solution in the context of the problem.

Answer 1

Part A:

n = 5q (1st equation)

0.05n + 0.25q = 2 (2nd equation)

Part B:

q = 4 ⇒ n = 5 * 4 = 20

Part C:

Margie has 20 nickels and 4 quarters, for a total of $ 2.00

Explanation:

Let's recall that a nickel has a value of $ 0.05 and a quarter a value of $ 0.25.

Let n represent the number of nickels and q represent the number of quarters.

Part A:

Write a system of equations to represent the situation.

n = 5q (1st equation)

n * 0.05 + q * 0.25 = 2

0.05n + 0.25q = 2 (2nd equation)

Part B:

Replacing n in the 2nd equation to solve for q:

0.05n + 0.25q = 2

0.05 * 5q + 0.25q = 2

0.25q + 0.25q = 2

0.5q = 2

q = 2/0.5

q = 4 ⇒ n = 5 * 4 = 20

Part C:

Margie has 20 nickels and 4 quarters, for a total of $ 2.00