252 m of pant cloth and 141 mof shirt cloth are available in a cloth store. To stitch one pant and one shirt, `2(1)/(2)` m and `1(3)/(4)` m of cloth are needed respectively. Then the approximate number of pants and shirts that can be made out of it are

Options

A. `(80,100)`
B. (100,80)
C. (100,90)
D. (90,80)

Answer

To solve the problem of how many pants and shirts can be made from the available cloth, we will follow these steps:

### Step 1: Determine the amount of cloth needed for one pant.
The cloth needed for one pant is given as \(2 \frac{1}{2}\) meters. We can convert this mixed number into an improper fraction:
\[ 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \text{ meters} \]

### Step 2: Calculate the number of pants that can be made.
We have a total of 252 meters of pant cloth available. To find out how many pants can be made, we divide the total cloth by the cloth needed for one pant:
\[ \text{Number of pants} = \frac{252}{\frac{5}{2}} = 252 \times \frac{2}{5} = \frac{504}{5} = 100.8 \]
Since we need the approximate number, we round \(100.8\) to \(100\).

### Step 3: Determine the amount of cloth needed for one shirt.
The cloth needed for one shirt is given as \(1 \frac{3}{4}\) meters. We convert this mixed number into an improper fraction:
\[ 1 \frac{3}{4} = 1 + \frac{3}{4} = \frac{4}{4} + \frac{3}{4} = \frac{7}{4} \text{ meters} \]

### Step 4: Calculate the number of shirts that can be made.
We have a total of 141 meters of shirt cloth available. To find out how many shirts can be made, we divide the total cloth by the cloth needed for one shirt:
\[ \text{Number of shirts} = \frac{141}{\frac{7}{4}} = 141 \times \frac{4}{7} = \frac{564}{7} \approx 80.57 \]
Again, rounding \(80.57\) gives us \(80\).

### Final Answer:
The approximate number of pants that can be made is \(100\) and the approximate number of shirts that can be made is \(80\).

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