Question

Ideal Body Weight The ideal body weight W for men (in kilograms) as a function of height h(in inches) is given by the function W(h) = 50 + 2.3(h – 60) (a) What is the ideal weight of a 6-foot male? (b) Express the height h as a function of weight W. (c) What is the height of a male who is at his ideal weight of 80 kilograms?

Answer 1

Hi,
a) In order to find the weight, we can substitute the corresponding height (6ft = 12*6 inches= 72 inches) into the equation. So from that we get:
W = 50 + 2.3(72 - 60) = 77.6kg
b) The question is basically asking us to rearrange the equation and solve for h:
W(h) = 50 + 2.3(h - 60)
W(h) - 50 = 2.3(h - 60)
\[\frac{ W(h) - 50 }{ 2.3 }=h-60\]
\[h=\frac{ W(h) - 50 }{ 2.3 }+60\]
c) We can use the equation from b and substitute the ideal weight ( W(h) = 80kg)
that would give us:
\[h=\frac{ 80 - 50 }{ 2.3 }+60\]
h = 73 inches = 6.1 ft

Hopefully that makes sense!