Answer :
Answer:
7350 boxes
Step-by-step explanation:
Solving the Problem
Find the Unit Rate
We're told that 5 machines after 8 hours can create 14,000 boxes. From this, we can find how many boxes are made by 1 machine in 1 hour.
We can divide the number of total boxes made by the number of machines, followed by the number of hours, though the order you divide can be switched without altering the unit rate.
[tex]\rm \dfrac{14000\:boxes}{5 \: machines} =2800\frac{boxes}{machine}[/tex],
this is the amount of boxes made after 8 hours from one machine.
[tex]\rm \dfrac{2800\frac{boxes}{machines} }{8\:hours} =350\frac{boxes}{machine\cdot hour}[/tex],
this is the number of boxes made by 1 machine in 1 hour.
[tex]\dotfill[/tex]
Getting the Final Answer
We're told to find the number of boxes by 7 machines in 3 hours, so we multiply the unit rate by 7 and 3!
[tex]\rm 350\frac{boxes}{machine\cdot hour} \cdot7 \: hours\cdot 3\: machines=7350\:boxes[/tex],
the metrics "hour(s)" and "machine(s)" cancel out, thus confirming that our answer and the method of solving it are correct.
