Let's solve this problem step by step.
1. Identify key values:
- The company packs [tex]\( x \)[/tex] boxes per hour.
- Each box contains 150 pins.
2. Calculate the number of pins packed per hour:
- Since each box contains 150 pins, if the company packs [tex]\( x \)[/tex] boxes in one hour, the total number of pins packed per hour is:
[tex]\[
\text{pins per hour} = 150 \, \text{pins/box} \times x \, \text{boxes/hour} = 150x \, \text{pins/hour}
\][/tex]
3. Convert the number of pins packed per hour to pins packed per minute:
- There are 60 minutes in one hour. Therefore, to find pins per minute, we divide the total number of pins packed per hour by 60:
[tex]\[
\text{pins per minute} = \frac{150x \, \text{pins/hour}}{60 \, \text{minutes/hour}} = \frac{150x}{60} \, \text{pins/minute}
\][/tex]
4. Simplify the fraction:
- Simplify the fraction [tex]\( \frac{150x}{60} \)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 30:
[tex]\[
\frac{150x}{60} = \frac{150 \div 30 \cdot x}{60 \div 30} = \frac{5x}{2}
\][/tex]
5. Conclusion:
- Therefore, the company packs:
[tex]\[
\frac{5x}{2} \text{ pins per minute}
\][/tex]
This shows that if the company packs [tex]\( x \)[/tex] boxes of pins per hour, it will pack [tex]\( \frac{5x}{2} \)[/tex] pins per minute.
