Given that [tex]\( y \)[/tex] varies inversely with [tex]\( x \)[/tex], and [tex]\( y \)[/tex] is 3 when [tex]\( x \)[/tex] is 11, what is [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is 3?

[tex]\( y = \, ? \)[/tex]



Answer :

To find the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is 3, given the relationship that [tex]\( y \)[/tex] varies inversely with [tex]\( x \)[/tex], we can follow these steps:

1. Understand the inverse variation: When [tex]\( y \)[/tex] varies inversely with [tex]\( x \)[/tex], it means [tex]\( y = \frac{k}{x} \)[/tex], where [tex]\( k \)[/tex] is a constant. This relationship means that the product of [tex]\( y \)[/tex] and [tex]\( x \)[/tex] is always the same constant value [tex]\( k \)[/tex].

2. Determine the constant [tex]\( k \)[/tex]: We are given that [tex]\( y = 3 \)[/tex] when [tex]\( x = 11 \)[/tex]. Using the inverse variation formula, we can set up the equation:
[tex]\[ 3 = \frac{k}{11} \][/tex]
We solve for [tex]\( k \)[/tex] by multiplying both sides of the equation by 11:
[tex]\[ k = 3 \times 11 = 33 \][/tex]
So, the constant [tex]\( k \)[/tex] is 33.

3. Find the new value of [tex]\( y \)[/tex]: Now we need to find the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is 3. Using the inverse variation formula again with the calculated constant [tex]\( k \)[/tex]:
[tex]\[ y = \frac{33}{3} \][/tex]
Dividing 33 by 3, we get:
[tex]\[ y = 11 \][/tex]

Therefore, when [tex]\( x \)[/tex] is 3, the value of [tex]\( y \)[/tex] is [tex]\( 11 \)[/tex].