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.
