A machine produces chocolates at a constant rate. In 42 minutes, the machine produces 7 pounds of chocolates. How long, in minutes, will it take the machine to produce 9 pounds of chocolates?



Answer :

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.