Answer:
11. D. May 20
12. C. Every 70 bags
Explanation:
11.
Mark on the calendar what days she has swimming and what days she has diving. (See picture below) Red is Swimming and blue is diving. For swimming, count by 5s. For diving, count by 3s. Find the next square that has both red and blue on it.
Therefore, she has both swimming and diving lessons on May 20th.
12.
Use least common multiples.
Count by 7s and 10s until there is a number that's the same.
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22....... You do not need to count by 2s. This is because you need to have a number that can also be counted to by 10s (a number with 10 as its factor), and 2 reaches all the multiples of 10. It is like 10 already includes 2.
7, 14, 21, 28, 35, 42, 49, 56, 63, 70
10, 20, 30, 40, 50, 60, 70
Therefore, every 70 bags will have all three items.