c) A garrison of 200 men has provisions for 45 days. For how many men
would the provisions last only for 30 days? wo. 1 days?

Question

c) A garrison of 200 men has provisions for 45 days. For how many men would the provisions last only for 30 days? wo. 1 days?

UpStudy AI · Accepted Answer

Let's denote the number of men in the garrison as $$ x $$.

Given:
- Number of men in the garrison = 200
- Provisions for 45 days
- Provisions for 30 days

We can set up a proportion to solve this problem:

$$
\frac{200 \text{ men}}{45 \text{ days}} = \frac{x \text{ men}}{30 \text{ days}}
$$

Now, we can solve for $$ x $$ using the proportion.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{200}{45}=\frac{x}{30}$$
- step1: Reduce the fraction:
  $$\frac{40}{9}=\frac{x}{30}$$
- step2: Swap the sides:
  $$\frac{x}{30}=\frac{40}{9}$$
- step3: Multiply both sides of the equation by $$30:$$
  $$\frac{x}{30}\times 30=\frac{40}{9}\times 30$$
- step4: Multiply the terms:
  $$x=\frac{40\times 30}{9}$$
- step5: Evaluate:
  $$x=\frac{400}{3}$$
The number of men for whom the provisions would last for 30 days is $$ x = \frac{400}{3} $$ or approximately 133.33 men.

Therefore, the provisions would last for 30 days for approximately 133 men.
The provisions would last for 30 days for approximately 133 men.

c) A garrison of 200 men has provisions for 45 days. For how many men
would the provisions last only for 30 days? wo. 1 days?

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