Question

Assume that y varies inversely with x. If y=7 when x=2/3, find y when x=7/3

Answer 1

Answer:

When x= 7/3, y = 2.

Step-by-step explanation:

When two variables are inversely related, it means that if one variable increases, the other one decreases. This relationship can be expressed as:

y = k/x, where "x" and "y" are variables and "k" the proportionality constant.

As the problem states, if y= 7 then x = 2/3. Now we can find the value of the constant "k"

7 = k/(2/3) ⇒ 7 x (2/3) = k ⇒ 14/3 = k.

So the equation for "x" and "y" ⇒ y = 14/3x

Finally you have to replace x = 7/3

⇒ y = 14/[3 x (7/3)] ⇒ y = 2.

Summarizing, when x = 7/3, y = 2.

Answer 2

Y=k/x
7=k/(2/3)
7=k(3/2)
times both sides by 2/3
14/3=k

y=(14/3)/x
y=(14/3)/(7/3)
y=(14/3)(3/7)
y=2