Inverse Variation Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

medium
If \(y = k/x\) and \(y = 12\) when \(x = 5\), find \(y\) when \(x = 15\).

Solution

  1. 1
    \(k = xy = 12 \times 5 = 60\).
  2. 2
    \(y = 60/15 = 4\).

Answer

\(y = 4\)
\(k = 60\); as \(x\) triples (5→15), \(y\) becomes one-third (12→4).

About Inverse Variation

A relationship where y=kxy = \frac{k}{x}: as one quantity doubles, the other halves—their product stays constant.

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More Inverse Variation Examples

Example 1 medium

(y) varies inversely with (x), and (y = 8) when (x = 3). Find (k) and the equation. Then find (y) wh

Example 2 hard

Speed and travel time are inversely proportional for a fixed distance. At 60 km/h the trip takes 4 h

Example 4 hard

The pressure (P) and volume (V) of a gas at constant temperature satisfy (PV = k). If (P = 4) atm wh

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