Inverse Quantity Math Example 4

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Example 4

medium
Variables xx and yy are inversely proportional. When x=4x = 4, y=9y = 9. Find yy when x=12x = 12, and find xx when y=6y = 6.

Solution

  1. 1
    Constant: k=4×9=36k = 4 \times 9 = 36.
  2. 2
    When x=12x = 12: y=3612=3y = \dfrac{36}{12} = 3.
  3. 3
    When y=6y = 6: x=366=6x = \dfrac{36}{6} = 6.

Answer

y=3y = 3 when x=12x = 12; x=6x = 6 when y=6y = 6.
For any inverse proportion, find the constant product k=xyk = xy from the given pair, then use xy=kxy = k to find missing values. Larger xx gives smaller yy and vice versa, always maintaining the same product.

About Inverse Quantity

The reciprocal or multiplicative inverse of a quantity, where multiplying a number by its inverse yields one. Inverse quantities appear whenever two measurements are inversely related, so that doubling one halves the other.

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More Inverse Quantity Examples

Example 1 easy

If [formula] workers can complete a job in [formula] days, how many days will it take [formula] work

Example 2 medium

The pressure [formula] of a gas varies inversely with its volume [formula] at constant temperature (

Example 3 easy

At [formula] km/h a trip takes [formula] hours. How long does the same trip take at [formula] km/h?

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