To find the solution to the problem, we first need to determine the ratio of jumping jacks to sit-ups based on Monday's workout.
On Monday:
- Jumping jacks = 54
- Sit-ups = 18
To find the ratio of jumping jacks to sit-ups, we divide both numbers by their greatest common divisor, which in this case is 18:
- Ratio = 54/18 : 18/18 = 3 : 1
This means that for every 3 jumping jacks Marco does, he does 1 sit-up.
Now, if Marco does 66 jumping jacks on Tuesday, we can determine how many sit-ups he will do:
Using the ratio 3:1:
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Let x be the number of sit-ups Marco does. According to the ratio of 3:1, we can set up the following proportion:
\[ \frac{66}{x} = \frac{3}{1} \]
Cross-multiplying gives us:
\[ 3x = 66 \]
Dividing both sides by 3, we find:
\[ x = \frac{66}{3} = 22 \]
So, if Marco does 66 jumping jacks on Tuesday, he will also have done 22 sit-ups that same day.
Now for Wednesday, Marco begins his workout with 15 sit-ups. Based on the ratio of jumping jacks to sit-ups (3:1), we need to determine how many jumping jacks he finishes with.
If he does 15 sit-ups, we can find how many jumping jacks that corresponds to using the same ratio. We'll let y be the number of jumping jacks. According to the ratio:
\[ \frac{y}{15} = \frac{3}{1} \]
Cross-multiplying gives us:
\[ y = 3 \times 15 = 45 \]
So, Marco finishes his workout on Wednesday by doing 45 jumping jacks.
In summary:
- If Marco does 66 jumping jacks on Tuesday, he will also have done 22 sit-ups.
- Marco begins his workout on Wednesday with 15 sit-ups and finishes the workout by doing 45 jumping jacks.
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