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Linear Equations in One Variable

SAT Math· difficulty 5/5

A coin collection has nickels, dimes, and quarters. Total = 50 coins, total value = \5.50$. There are twice as many nickels as quarters. How many quarters?

  • A

    20

  • B

    15

  • C

    5

  • D

    10

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Explanation

n=2qn = 2q, n+d+q=50n + d + q = 50, 0.05n+0.10d+0.25q=5.500.05n + 0.10d + 0.25q = 5.50. Sub n=2qn = 2q: 3q+d=503q + d = 50, so d=50−3qd = 50 - 3q. Value: 0.10q+0.10(50−3q)+0.25q=5.500.10q + 0.10(50 - 3q) + 0.25q = 5.50 → 0.05q+5=5.500.05q + 5 = 5.50 → q=10q = 10.

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