Answer:
1/2
Step-by-step explanation:
x is directly proportional to y (this means y will go on top because of the directly part) and inversely proportional to z (this means z will go on bottom due to the inversely part).
There is a constant k such that:
.
Contant means it will never change. It will not care what (x,y,z) you use, it will remain the same.
We will use the first point to find k and then that k will still be there no matter what (x,y,z) they give you.
We have (1/2 , 3/4 , 2/3) is on our graph of the equation:
.
Insert the numbers:
Multiply both sides by :
Simplify left hand side:
Multiply both sides by 4:
Multiply both sides by 1/3 (or you can say divide by 3):
So k=4/9 no matter the (x,y,z).
We are asked to find x given y=7/8 and z=7/9.
Input these numbers:
Change the division to multiplication:
I see a 7 on top and bottom that I can cancel:
I see a 9 on top and bottom that I can cancel:
Let's go ahead and multiply and reduce more later if we can.
Multiply straight across on top.
Multiply straight across on bottom.
Divide top and bottom by 4: