Multiple choice

Abraham bought music concert tickets and Gold and Silver passes for $25 and $15, respectively. He bought a total of 100 passes for \$1,750. He sold some of the Silver passes to cover the extra expenses. Find the number of Silver passes he sold so that the average amount (arithmetic mean) of the remaining passes becomes \$20.

  1. 40

  2. 45

  3. 50

  4. 55

  5. 60
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total cost = 1750, Total items = 100. Let G be number of Gold passes (\$25) and S be number of Silver passes (\$15). G + S = 100, 25G + 15S = 1750. Solving gives G = 25, S = 75. If he sells x silver passes, remaining passes = 100 - x. Total value = 1750 - 15x. Average = (1750 - 15x) / (100 - x) = 20. 1750 - 15x = 2000 - 20x. 5x = 250, x = 50.

AI explanation

Using the method of alligation or simultaneous equations for the 100 total passes, the number of Gold passes bought is 25 and the number of Silver passes bought is 75, totaling $1,750. Let S be the number of Silver passes sold. The total value of the remaining passes is 1750 minus 15S. The average value of the remaining 100 minus S passes is 20, so 1750 minus 15S equals 2000 minus 20S. Solving for S, we get 5S equals 250, so the number of Silver passes sold is 50.

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