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26 December, 06:25

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.

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Answers (1)
  1. 26 December, 06:45
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    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

    Step-by-step 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
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