A neighborhood is putting together holiday care baskets. There are 42 toys and 56 books. If each basket has...

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7. A neighborhood is putting together holiday care baskets. There are 42 toys and 56 books. If each basket has the same number of toys and books so that no toys or books are left over, what is the greatest number of baskets that could be made?
8. A neighborhood trash pick-up comes every 9 days, and recycling pick-up comes every 12 days. What is the fewest number of days in which 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 find the greatest common divisor (GCD) of 42 and 56. The prime factors of 42 are 2, 3, and 7. The prime factors of 56 are 2, 2, 2, and 7. The common factors are 2 and 7. Therefore, the GCD is 2 x 7 = 14. The greatest number of baskets that could be made is 14.
To find the fewest number of days in which both trash and recycling are picked up on the same day, we need to find the least common multiple (LCM) of 9 and 12. The prime factors of 9 are 3 and 3. The prime factors of 12 are 2, 2, and 3. The LCM is 2 x 2 x 3 x 3 = 36. Therefore, the fewest number of days is 36.
Reid is correct. The Venn diagram shows the prime factors of 56 as 2, 2, 7 and the prime factors of 42 as 2, 3, 7. The common factors are 2 and 7, which are correctly placed in the intersection. However, the diagram incorrectly places a 2 in the intersection twice. The correct prime factors should be: 56 = 2, 2, 2, 7 and 42 = 2, 3, 7. The correct intersection should only include one 2 and one 7. Therefore, Addie's diagram is incorrect.

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A neighborhood is putting together holiday care baskets. There are 42 toys and 56 books. If each basket has...

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