Question

The recommended weight for an adult male is given by the formula \(w=\frac{11}{2} h-220,\) where w represents the recommended weight in pounds and \(h\) represents the height of the person in inches. Determine the height of an adult male whose recommended weight is 165 pounds.

Short answer

Answer: The height of an adult male with a recommended weight of 165 pounds is 70 inches.

Step-by-step solution

Write down the given formula

The formula for the recommended weight \((w)\) for an adult male based on their height \((h)\) is \(w=\frac{11}{2}h-220\).

Substitute the target weight into the formula

We are given an adult male whose recommended weight is 165 pounds, so we substitute \(w=165\) into the formula: $$165= \frac{11}{2}h-220$$

Solve the equation for the height variable h

We will now solve the equation for \(h\). First, add 220 to both sides of the equation: $$165+220= \frac{11}{2}h$$ $$385= \frac{11}{2}h$$ Next, multiply both sides by the reciprocal of the coefficient of \(h\), which is \(\frac{2}{11}\): $$\frac{2}{11} \times 385 = \frac{2}{11} \times \frac{11}{2}h$$ Simplify the equation to find the value of \(h\): $$h = 70$$

State the solution

An adult male with a recommended weight of 165 pounds would have a height of 70 inches.