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Pike Vitamin Shop sold equal quantities of Vitamin A and Vitamin D supplements this morning, even though the Vitamin A supplements come in packs of 44 and the Vitamin D supplements in packs of 77. What is the smallest number of each type that the store could have sold?\newline_____\_\_\_\_\_ supplements

Full solution

Q. Pike Vitamin Shop sold equal quantities of Vitamin A and Vitamin D supplements this morning, even though the Vitamin A supplements come in packs of 44 and the Vitamin D supplements in packs of 77. What is the smallest number of each type that the store could have sold?\newline_____\_\_\_\_\_ supplements
  1. Identify Problem Type: Step 11: Identify the problem type. We need to find the smallest number of each supplement type that could be sold in equal quantities, given different pack sizes. This is a Least Common Multiple (LCM) problem.
  2. Calculate LCM: Step 22: Calculate the LCM of the pack sizes. The pack sizes are 44 for Vitamin A and 77 for Vitamin D.\newline- List the multiples of 44: 4,8,12,16,20,24,28,32,36,404, 8, 12, 16, 20, 24, 28, 32, 36, 40\ldots\newline- List the multiples of 77: 7,14,21,28,35,42,497, 14, 21, 28, 35, 42, 49\ldots\newline- The smallest common multiple is 2828.
  3. Verify Solution: Step 33: Verify the solution. Since 2828 is a multiple of both 44 and 77, it is the correct LCM. This means the store could have sold 2828 packs of each supplement.

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