two machines can complete 8 tasks every 3 days. let "t" represent the number of tasks these machines can complete in 30 day month

Question

write a proportion to show this example

Answer 1

The machines complete tasks at the same speed, whether it's over the course of 3 days, a month, a minute, whatever. That's why the proportions work, because they go at the same speed always.

 

the speed is: 8 tasks/3 days = t tasks/30 days

 

There are a few ways we can solve this:

 

In order for these to be equal, these must be equivalent fractions. That means that whatever the relationship between numerator and denominator on one side of the equation, it must be the same on the other side. On the left side of the equation, we get from the denominator to the numerator by multiplying by 8/3, so it must also be the case on the right side. 30×(8/3)=240/3=80

 

Another way we can solve for t is to say that whatever the relationship between the two denominators, it must also be the relationship between the two numerators. In this case, we get from the denominator 3 to 30 by multiplying by ten, so it must also be the case with the numerators. 8×10=80

 

Finally, for more complicated proportions, we can cross multiply. This method says that the top left times the bottom right equals the bottom left times the top right. It is called cross multiplication because if you circle the things you are multiplying (which I recommend, to keep track), it makes a big cross. In this case, 8×30=3×t

8×30=3×t

240=3t

80=t