Multiple choice

A toy manufacturer produces toys at a cost of $15 each and sells them at a 40% markup on cost during the regular season. During the holiday season, the manufacturer offers a 25% discount on the selling price to boost sales volume. If the manufacturer's overall markup on cost for all toys sold is 30 percent, what percent of the total units were sold during the holiday season?

  1. 22.6%

  2. 26.8%

  3. 28.6%

  4. 62.8%

  5. 68.2%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Cost = 15. Regular price = 15 * 1.4 = 21. Holiday price = 21 * 0.75 = 15.75. Overall markup = 30%, so average selling price = 15 * 1.3 = 19.5. Let x be the fraction of units sold during the holiday. 21(1-x) + 15.75x = 19.5. 21 - 21x + 15.75x = 19.5. 1.5 = 5.25x. x = 1.5 / 5.25 = 150 / 525 = 2/7 approx 0.2857 or 28.6%.

AI explanation

Let the cost price be \$15, so the regular selling price is 1.4 times 15, which equals \$21. During the holiday season, the selling price is 0.75 times 21, which equals $15.75. Using the method of alligation, the regular season profit percentage is 40% and the holiday season profit percentage is (15.75 minus 15) divided by 15, which equals 5%. The overall desired profit is 30%, so the ratio of regular season to holiday season sales volume is (30 minus 5) to (40 minus 30), giving a 25 to 10 ratio. The percentage of total units sold during the holiday season is 10 divided by 35, which equals 28.6 percent.

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