1.3 Mathematical Modeling

Mathematical ModelingThe process of translating phrases or

sentences to algebraic expressions or equations

Steps1- Draw a Diagram

2- Set up and equation3- Solve the equation

4- Check the solutions to see if they make sense

Example 1

You have accepted a job for which your annual salary will be $27,236.

This salary includes a year-end bonus of $500. If you are paid twice a month, what will your gross pay be

for each paycheck?

Example 2

You have accepted a job that pays $8 an hour. You are told that after a 2

month probationary period, your hourly wage will be increased to $9

an hour. What percent raise will you receive after the 2-month period?

Example 3

Your annual salary is $24,000. In addition to your salary, your employer also pays for the

following benefits: employer’s portion of Social Security ($1836),worker’s compensation ($120), unemployment compensation ($180), medical insurance ($2240), and retirement contribution ($1560).

The total value of the benefits package represents what percent of your annual salary?

Example 4

A rectangular family room is twice as long as it is wide, and its perimeter is 84 feet. Find the dimensions of

the family room.

Example 5

A plane is flying nonstop from new York to San Francisco, a distance of about

2700 miles. After an hour and a half in the air, the plane flies over Chicago (a distance of 800 miles from New York). Estimate the time it will take the plane to fly from New York to San Francisco.

Example 6To measure the height of a New York

City skyscraper, you measure the shadow cast by one of the buildings and find it to be 170.25 feet long. Then you measure the shadow cast by a 4-foot post and find it to be 6

inches long. Estimate the building’s height.

Example 7

You invest a total of $10,000 at 4.5% and 5.5% simple interest. During one year the two accounts earned

$508.75. How much did you invest in each? (Interest formula: I = Prt )

Example 8

A store has $30,000 of inventory in 32-inch and 40-inch color

televisions. The profit on a 32-inch set is 22% and the profit on a 40-inch set is 40%. The profit for the

entire stock is 35%. How much was invested in each type of television?

Example 9

A cylindrical can has a volume of 300 cubic centimeters and a radius of 3 centimeters. Find the height of the

can.