Question

20 points! Brainliest! Need help

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


Write a system of equations to represent the situation. Let n represent the number of nickels and q represent the number of quarters.

Solve the system you wrote in part (a). Show your work.

Interpret your solution in the context of the problem.

Answer 1

Answer:

• n = 5q; 25q+5n = 200
• (n, q) = (20, 4)
• Margie has 20 nickels and 4 quarters

Step-by-step explanation:

a) Using the defined variables, we can translate the problem statements to equations:

• n  = 5q . . . . Margie has 5 times as many nickels as quarters
• 25q + 5n = 200 . . . . the total value of Margie's coins is 200 cents

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b) Substituting for n, we have ...

  25q +5(5q) = 200

  50q = 200 . . . . . . . collect terms

  q = 200/50 = 4 . . . divide by the coefficient of q

  n = 5·4 = 20

The solution is (n, q) = (20, 4).

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c) Since n represents the number of nickels Margie has, n=20 means Margie has 20 nickels. Similarly, q=4 means Margie has 4 quarters.