Question

A machine in a factory makes paper clips. The table shows he proportional relationship between the number of paper clips a machine makes and the number of minutes it takes to make the paper clip. Enter the missing numbers in the table to show the proportional relationship number of paper clips: ___ ____ 330 440Number of minutes 3 5 6 ___

Answer 1

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx

where

k is the constant of proportionality

In this problem we have

x------> number of minutes

y -----> number of paper clips

so

step 1

Find the value of k

K=y/x

looking at the table

we have

For x=6 -----> y=330

substitute

k=330/6

k=55

The linear equation that represent this situation is

y=55x

step 2

Find the missing values

For x=3

substitute in the equation

y=55(3)

y=165 paper clips

For x=5

y=55(5)

y=275 paper clips

For y=440

substitute in the equation

440=55x

solve for x

x=440/55

x=8 minutes