You can put this solution on YOUR website! "y varies directly as x", by itself, means:
And "y varies inversely as z", by itself means:
In both equations, the "k" is some constant number which is called the constant of variation.
"y varies directly as x and inversely as z", combined, means:
To solve your problem we will first need to find the "k". For this we take the fact that y = 3 when x = 5 and z = 15. Substituting these numbers in for x, y and z we get:
Now we solve for k. The fraction reduces:
Now we just multiply by 3:
So the constant of variation for our equation is 9:
Now that we know k, our equation is:
We can use this to find y when x = 7 and z = 8:
which simplifies to:
or, if you don't like improper fractions:
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