MATH SOLVE

10 months ago

Q:
# 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

A:

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.

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.