A holiday toy drive is putting together baskets for charity. There are 84 toys and 56 books. If each basket...

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7. A holiday toy drive is putting together baskets for charity. There are 84 toys and 56 books. If each basket will receive the same number of toys and books, that no toy or book is left over, then what is the greatest number of baskets that could be made?
8. A neighborhood trash pick-up comes every 8 days while the recycling pick-up is every 12 days. When the next day will both the trash and recycling be picked up on the same day?
9. Addie organizes the Venn diagram below showing the prime factors of 56 and 42. Reid says that she is incorrect. Who is correct? Justify your thinking.

SnapAndSolve AI · Accepted Answer

To find the greatest number of baskets, we need to determine the greatest common divisor (GCD) of 84 and 56. The prime factors of 84 are 2, 2, 3, and 7. The prime factors of 56 are 2, 2, and 7. The common factors are 2, 2, and 7. Therefore, the GCD is 2 x 2 x 7 = 28. The greatest number of baskets that could be made is 28.
To find when both trash and recycling will be picked up on the same day, we need to determine the least common multiple (LCM) of 8 and 12. The prime factors of 8 are 2, 2, and 2. The prime factors of 12 are 2, 2, and 3. The LCM is 2 x 2 x 2 x 3 = 24. Therefore, both will be picked up on the same day every 24 days.
The prime factors of 56 are 2, 2, 2, and 7. The prime factors of 42 are 2, 3, and 7. Addie's Venn diagram shows 56 with factors 2, 2, 7 and 42 with factors 2, 3, 7. Reid says she is incorrect. Addie is correct because the common factors are 2 and 7, and the diagram correctly shows these.

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A holiday toy drive is putting together baskets for charity. There are 84 toys and 56 books. If each basket...

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