# Math 221 Inequalities

Math 221: Introduction to Algebra

Instructor Jonah Mutua

June 16, 2013

Inequalities

This assignment involves the use of inequalities in mathematical equations. The formula for finding Body Mass Index (BMI) is BMI =703W/H^2.

In this formula W = weight in pounds

In this formula H = height in inches.

For this assignment four intervals based on our own personal heights must be calculated. I am 6 feet 4 inches tall. My height in inches (or H) equals 76. These intervals include inequalities that are categorized as between or compound inequalities. One interval in this assignment will be a regular inequality. Wherever “BMI” appears in the inequalities, we will exchange the formula and solve the inequality for W to find the weight ranges that fit each category for my height.

The first interval calculates those who might have a longer than average life span. The compound inequality for this follows:

17<BMI<22

17<703W/76^2<22

17<703W/5776<22

17*5776<703W<22*5776

98192<703W<127072 (Dividing all by 703)

139.6756<W<180.7567

140<W<181

People with a height of 76 inches may have a longer lifespan if they weigh between 140 and 181 pounds (after rounding up).

Now we will do something a little different from the previous problem. Below we will solve the 2nd inequality for the formula for W prior to entering the different values to find W.

23<703W/H^2<25

23H^2<703W<25H^2

Divide all by 703

23H^2/703<W<25H^2/703

Square H for insertion (76*76) = 5776

23(5776)/703<W<25(5776)/703

132848/703<W<144400/703

188.9729<W<205.4054

189<W<205

This inequality shows that people that are 76 inches tall and weigh between 189 and 205 are probably not overweight.

The efficiency of this method is more efficient than the first, so we will continue to employ this method. The 3rd interval is...

References: 1) http://vizedhtmlcontent.next.ecollege.com/pub/content/4720bf80-cc90-4155-9067-48cf5d83a5d7/MAT221.W2.AssignmentExample.pdf

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