Zachary's Stationery sells thank-you cards in packs of 10 and birthday cards in packages of 9. Surprisingly, the store sold the same number of each type of card this month. What is the minimum number of each card type that the store must have sold? _____ cards

Question

Zachary's Stationery sells thank-you cards in packs of 10 and birthday cards in packages of 9. Surprisingly, the store sold the same number of each type of card this month. What is the minimum number of each card type that the store must have sold?  _____ cards

Bytelearn · Accepted Answer

Identify the problem:  Step 1: Identify the problem. We need to find the minimum number of each type of card sold, given that the number of thank-you cards and birthday cards sold is the same. Determine mathematical approach:  Step 2: Determine the mathematical approach. Since the store sold the same number of thank-you cards and birthday cards, we need to find the least common multiple (LCM) of the pack sizes (10 for thank-you cards and 9 for birthday cards). Calculate the LCM:  Step 3: Calculate the LCM of 10 and 9. Factors of 10: 1, 2, 5, 10 Factors of 9: 1, 3, 9 LCM calculation: The LCM of 10 and 9 is the product of the highest power of all prime factors present in the numbers. Here, 10 = 2 x 5 and 9 = 3^2. So, LCM = 2 x 5 x 3^2 = 90.

Zachary's Stationery sells thank-you cards in packs of $10$ and birthday cards in packages of $9$ . Surprisingly, the store sold the same number of each type of card this month. What is the minimum number of each card type that the store must have sold? $\newline$ $\_\_\_\_\_$ cards

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Zachary's Stationery sells thank-you cards in packs of $10$ and birthday cards in packages of $9$ . Surprisingly, the store sold the same number of each type of card this month. What is the minimum number of each card type that the store must have sold? $\newline$ $\_\_\_\_\_$ cards