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? 

Accepted Solution

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.
[tex] \frac{X \;straws}{50 \;hours} =\frac{20,000 \;straws}{8 \;hours} \\\\\frac{X \;straws}{20,000 \;straws} =\frac{50 \;hours}{8 \;hours} \\\\\frac{X}{20,000} =\frac{50}{8} \\\\Cross \;multiplying \\\\8*X = 50*20000 \\\\8X = 1,000,000 \\\\\frac{8X}{8} =\frac{1,000,000}{8} \\\\X=125,000 \;straws [/tex]Hence, total 125,000 straws would be produced in 50 hours.