If y=10 when x=5, find y when x=2.

Question

Assume that y varies inversely as x. Write an inverse variation equation that relates x and y. Then solve.

Answer 1

Inverse variation between two quantities means that as one quantity increases/decreases, the other quantity does the opposite. One of the basic equations you can use for this type of problem is xy = k where "k" is the constant of variation; it's a value that stays fixed when the x and y quantities "do their thing".

We can start by finding "k" using the x and y values that were paired up with each other. Since y = 10 when x = 5, we can set up the equation as 5(10) = k and so "k" comes out to be 50. This value will stay fixed. So now we take the other x value that was given and, using the "k" value we just found, we set up a 2nd equation in the same form but this time we use it to find y. So the 2nd equation will be 2(y) = 50. Solving for y, this gives y = 25.

Answer 2

5/2 = y/10

2y = 50

y = 25