Question

the weight measured in pounds of a teenager boy can modeled as a function of his height measured in inches. the relationship between both variables is $w(h) = 3.5h - 108$.
a) find the value of $w(72)$. write a sentence to interpret your answer in the context of the problem.
b) solve the equation $w(h) = 120$. write a sentence to interpret your answer in the context of the problem.

Explanation:

Part (a)

Step1: Substitute \( h = 72 \) into \( w(h) \)

We have the function \( w(h)=3.5h - 108 \). Substitute \( h = 72 \) into the function:
\( w(72)=3.5\times72 - 108 \)

Step2: Calculate the value

First, calculate \( 3.5\times72 \): \( 3.5\times72 = 252 \). Then subtract 108: \( 252 - 108 = 144 \).

Interpretation: A teenage boy with a height of 72 inches is modeled to weigh 144 pounds.

Step1: Set up the equation

We know \( w(h) = 120 \) and \( w(h)=3.5h - 108 \), so set \( 3.5h - 108 = 120 \).

Step2: Solve for \( h \)

Add 108 to both sides: \( 3.5h=120 + 108 \), so \( 3.5h = 228 \). Then divide both sides by 3.5: \( h=\frac{228}{3.5}=\frac{2280}{35}=\frac{456}{7}\approx65.14 \) (or as a fraction, \( \frac{456}{7} \), or decimal \( \approx65.14 \)).

Interpretation: A teenage boy who weighs 120 pounds is modeled to have a height of approximately 65.14 inches (or \( \frac{456}{7} \) inches).

Answer:

(for part a):
\( w(72)=144 \)

Part (b)