Y varies inversely as x, and y = 50 when x = 10. What is the value of y when x = 20?

1 Answer
Jun 6, 2016

When x=20x=20 the value of color(purple)(y = 25y=25

Explanation:

Method 1:
In an inverse variation as one variable increases the other decreases.
color(blue)(yprop1/xy1x

We now insert a constant kk into the equation:

y = k * 1/xy=k1x

color(blue)(y = k /xy=kx

We now substitute the value of variables as provided:

x=10 , y =50x=10,y=50

50 = k /1050=k10

k = 50 * 10 = color(green)(500k=5010=500

Now we use the value of this constant to find y:y:
As per data provided x =20x=20
color(blue)(y = k /xy=kx

y = 500 /20y=50020

color(purple)(y = 25y=25

Method 2:

As per data provided when color(green)(x =10)x=10 , y =50y=50

So, when x =20x=20, the value is doubled from the initial value of xx,
(20 = color(green)(10) * 2)20=102)

Since the value of xx is doubled , the value of yy will have to be halved from the initial value, since there is an inverse variation.

So, y = 50/2, color(purple)(y = 25y=502,y=25