Question

The number of plastic straws produced by a machine varies directly as the amount of time the machine is operating. If the machine produces 20,000 straws in 8 hours, how many straws can it produce in 50 hours?

Answer 1

Given is the direct relationship between number of produced straws and the hours of operating machine.

Given that 20,000 straws are produced in 8 hours of machine's operation.

Let's assume that 'x' straws are produced in 50 hours of machine's operation.

Using the concept of proportions, x straws in 50 hours would be proportional to 2000 straws in 8 hours.

`(X \;straws)/(50 \;hours) =(20,000 \;straws)/(8 \;hours) \\\\(X \;straws)/(20,000 \;straws) =(50 \;hours)/(8 \;hours) \\\\(X)/(20,000) =(50)/(8) \\\\Cross \;multiplying \\\\8*X = 50*20000 \\\\8X = 1,000,000 \\\\(8X)/(8) =(1,000,000)/(8) \\\\X=125,000 \;straws`

Hence, total 125,000 straws would be produced in 50 hours.