To determine how long it will take the machine to produce 9 pounds of chocolates, we can follow a step-by-step method:
1. Understand the given information:
- The machine can produce 7 pounds of chocolates in 42 minutes.
2. Calculate the rate of production:
To find out the rate at which the machine produces chocolate, we need to determine how many minutes it takes to produce one pound of chocolate.
[tex]\[
\text{Rate per pound} = \frac{\text{Time to produce 7 pounds}}{\text{Number of pounds}} = \frac{42 \text{ minutes}}{7 \text{ pounds}}
\][/tex]
3. Perform the division to find rate per pound:
[tex]\[
\frac{42 \text{ minutes}}{7 \text{ pounds}} = 6 \text{ minutes per pound}
\][/tex]
This means it takes the machine 6 minutes to produce one pound of chocolate.
4. Determine the time to produce the target amount:
Next, we need to find out how many minutes it will take to produce 9 pounds of chocolates. Given that the machine takes 6 minutes to produce one pound, the total time to produce 9 pounds is:
[tex]\[
\text{Time to produce 9 pounds} = 6 \text{ minutes/pound} \times 9 \text{ pounds}
\][/tex]
5. Perform the multiplication:
[tex]\[
6 \text{ minutes/pound} \times 9 \text{ pounds} = 54 \text{ minutes}
\][/tex]
Therefore, it will take the machine 54 minutes to produce 9 pounds of chocolates.
To summarize:
- The machine produces chocolates at a rate of 6 minutes per pound.
- It will take 54 minutes to produce 9 pounds of chocolates.
