SOLUTION: I am having issues figuring out the inverse variation. Here is the problem Suppose z varies inversely with t and that z=12 and t=10. What is the value of z when t = 6

Algebra ->  Equations -> SOLUTION: I am having issues figuring out the inverse variation. Here is the problem Suppose z varies inversely with t and that z=12 and t=10. What is the value of z when t = 6      Log On


   

Question 192180: I am having issues figuring out the inverse variation. Here is the problem
Suppose z varies inversely with t and that z=12 and t=10. What is the value of z when t = 6
Found 2 solutions by RAY100, jim_thompson5910:
Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
z= k/t
12 =k/10
cross multiply
k=120
now proportion is
z=120/t
for t=6
z=120/6 = 20

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"z varies inversely with t" in English means that as "t" increases, "z" decreases. On the flip side, as "t" decreases, "z" increases. So as one goes up, the other goes down (and vice versa)


So algebraically, this means that z=k%2Ft where "k" is some unknown constant. The goal is to find "k"


Since we're given that "z=12 and t=10", this means that we can plug them into the equation above to find "k"


z=k%2Ft Start with the given equation


12=k%2F10 Plug in z=12 and t=10


12%2A10=k Multiply both sides by 10


120=k Multiply


So the constant "k" is k=120


This means that our original equation is z=120%2Ft


Q: "What is the value of z when t = 6?"


z=120%2Ft Start with the last equation


z=120%2F6 Plug in t = 6


z=20 Reduce


So z = 20 when t = 6