Drew does push-ups every three days starting on 3 January. He does sit-ups every four days starting on January 4, On which days in January will he do both push-ups and sit-ups? Use words, numbers, or models to justify your answer

push ups: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

sit ups: 4, 8, 12, 16, 20, 24, 28

January 24

12,24

It is january 24

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yes January 24th is right

24

January

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To determine on which days in January Drew will do both push-ups and sit-ups, we can create a visual model.

First, let's list down the days in January:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31

Now, let's mark the days where Drew will do push-ups. According to the given information, Drew does push-ups every three days starting on January 3. So, we start by marking January 3 as a push-up day. The next push-up day will be January 6 (3 days later), then January 9 (3 days after that), and so on. We can mark these push-up days with 'P':

1, 2, P, 4, 5, P, 7, 8, P, 10, 11, P, 13, 14, P, 16, 17, P, 19, 20, P, 22, 23, P, 25, 26, P, 28, 29, P, 31

Next, let's mark the days where Drew will do sit-ups. According to the given information, Drew does sit-ups every four days starting on January 4. So, we start by marking January 4 as a sit-up day. The next sit-up day will be January 8 (4 days later), then January 12 (4 days after that), and so on. We can mark these sit-up days with 'S':

1, 2, P, S, 5, P, 7, S, P, 11, 13, P, S, 16, 17, P, 19, S, P, 23, 25, P, S, 28, 29, P, 31

Now, looking at the marked days, we can see that the days highlighted with both 'P' and 'S' are:

S: 11, 23
P: 13

Therefore, Drew will do both push-ups and sit-ups on January 11, 13, and 23 in January.

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