The number of widgets that a manufacturing plant can produce varies jointly as the number of workers and the time that they have worked.

Question

1) Find the constant of proportionality, k, to 2 decimal places if 445 workers work 18 hours and can produce 57271.5 widgets.

k = 

2) How many widgets (to the nearest tenth) can be produced by 475 workers in 20 hours?

Widgets = 

Answer 1

Hi, there.

1) realize this problem uses a varies directly formula in form of y=kx but with two variables that go after the constant k. As a result,here, I get the formula y=kwt. The two variables in this formula is w and t.

2) We need to first find k. Now with k solved it looks this y÷wt=k. W stands # of workers, t stands for number of hours(time), y stands for the number of widgets. So, w=445, t=18. Go ahead and plug the values for y,w and t. Then k should equal 7.15

3) Now rewrite y=kwt to y=7.15wt

4) figure out what y is. So, y=7.15(475)(20)

y=67,925. This looks about right because the final number of widgets should be more than 57,271.5 because there are more workers and hours. There are 67,925 widgets. This is the answer