If y is inversely proportional to x, and if y = 15 when x = 23 then 15/1 = k/23^3 = 15/1 = k/12167, y ∝ x−1 = 15 ∝ k/12167
How do we express this in inverse proportion?
Given, y is inversely proportional to x
or
y ∝ x−1
this is if and only if y ∝ 1/x
y = 1/xk
Also, we know that if y = 15 when x = 23^3
then 15/1 = k/23^3
⇔
multiply both sides by 23
345 = k this is our constant of proportionality
⇒
this gives us our formula
y = 345/x
Then consider when y = 15
then
15 = 345/x
⇔
multiply both sides by x
15x = 345
⇔
divide both sides by 15
x = 23
Therefore, the correct answer is as given above
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