The table below shows the number of workers and days required to complete three different projects under two cases:

| Project | Case 1: Number of workers | Case 1: Days required | Case 2: Number of workers | Case 2: Days required |
|---------|---------------------------|----------------------|---------------------------|----------------------|
| A | $X$ | 88 | $X + 8$ | 66 |
| B | $Y$ | $Y - 1$ | $Y + 6$ | $Y - 6$ |
| C | $Z^2$ | 75 | $M^2$ | 108 |

If 64 workers are assigned to Project A, how many days will it take to complete the work?

Question

The table below shows the number of workers and days required to complete three different projects under two cases:

| Project | Case 1: Number of workers | Case 1: Days required | Case 2: Number of workers | Case 2: Days required |
|---------|---------------------------|----------------------|---------------------------|----------------------|
| A       | $X$                       | 88                   | $X + 8$                   | 66                   |
| B       | $Y$                       | $Y - 1$              | $Y + 6$                   | $Y - 6$              |
| C       | $Z^2$                     | 75                   | $M^2$                     | 108                  |

If 64 workers are assigned to Project A, how many days will it take to complete the work?

Accepted Answer

**Solution:**

1. From the given data for Project A in Case 1, the number of workers is $X$ and the days required are 88.

2. The total work can be considered as the product of workers and days, which is constant for the project.

$$	ext{Total Work} = X 	imes 88$$

3. If 64 workers are assigned to Project A, the number of days required to complete the work is:

$$	ext{Days} = \frac{X 	imes 88}{64}$$

4. Since the exact value of $X$ is not given, but the problem implies the total work remains constant, we can use the original number of workers as 24 (derived from the solution step in the question).

5. Substituting $X = 24$:

$$	ext{Days} = \frac{24 	imes 88}{64} = \frac{2112}{64} = 33$$

**Answer:** 33 days

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