Inequality word problem

Question

Forensic scientists use the equation h=2.6f +47.2 to estimate the height h of a woman given the length in centimeters f of her femur bone.

a.) suppose the equation has a margin or error of + with a minus sign under it 3 centimeters. Write an inequality to represent the height of a woman given the length of her femur bone.

 

b.) If the length of a female skeleton's femur is 50 centimeters, write and solve an absolute value inequality that describes the woman's height in centimeters.

 

 

Answer 1

The solution to part a.) Write an inequality to represent the height of a woman given the length of her femur bone.is ∣ h−(2.6f+47.2) ∣≤3

The solution to part b.)  If the length of a female skeleton's femur is 50 centimeters, write and solve an absolute value inequality that describes the woman's height in centimeters.

Since the femur length ff is 50 centimeters, first you have to we calculate the estimated height: h=2.6(50)+47.2

2.6×50 = 130

130+47.2 = 177.2

Therefore, the estimated height is 177.2 cm.

Given a margin of error of plus or minus 3 cm, the absolute value inequality for h would then be

∣ h−177.2 ∣≤3