College Algebra Chapter 1 Equations and Inequalities Section 1.2 Applications with Linear and Rational Equations Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

Problem Solving Strategy Read the problem carefully. Determine what the problem is asking for, and assign variables to the unknown quantities. Make an appropriate figure or table if applicable. Label the given information and variables in the figure or table. Write an equation that represents the verbal model. The equation may be a known formula or one that you create that is unique to the problem. Solve the equation from Step 3. Interpret the solution to the equation and check that it is reasonable in the context of the problem.

Concepts Solve Applications Involving Simple Interest Solve Applications Involving Mixtures Solve Applications Involving Uniform Motion Solve Applications Involving Rate of Work Done Solve Applications Involving Proportions

Concept 1 Solve Applications Involving Simple Interest

Example 1 Carlos borrowed a total of $8,000 from his mom and a bank to start a food truck business. The bank charged the equivalent of 5% simple interest. His mom charged a much better rate equivalent to 1% simple interest, but made him promise to call more often. If the total interest after 1 year was $280, determine the amount Carlos borrowed from his mom and the bank.

Skill Practice 1 Franz borrowed a total of $10,000. Part of the money was borrowed from a lending institution that charged 5.5% simple interest. The rest of the money was borrowed from a friend to whom Franz paid 2.5% simple interest. Franz paid his friend back after 9 months (0.75 year) and paid the lending institution after 2 yr. If the total amount Franz paid in interest was $735, how much did he borrow from each source?

Concept 2 Solve Applications Involving Mixtures

Example 2 Putting together snacks for a party, Alicia combines a low fat trail mix with a very tasty higher fat candy mix. How much of the 10% fat trail mix should she mix with 4 ounces of the 40% fat candy mix to get a 12% fat party mix? 10% trail mix 40% candy mix 12% party mix amount of mix pure fat

Skill Practice 2 How much 4% acid solution be mixed with 200 mL of a 12% acid solution to make a 9% acid solution?

Concept 3 Solve Applications Involving Uniform Motion

Example 3 Daryl and Cynthia leave home at 7 am, heading in opposite directions for work. Daryl usually spends 30 minutes biking to work while Cynthia needs only 20 minutes to walk to work. Cynthia's average speed is 7 miles per hour slower than Daryl's average speed. If they work 6 miles apart, what is the average speed, in miles per hour, for each person? Distance Rate Time Daryl Cynthia

Skill Practice 3 Rene drove from Miami to Orlando, a total distance of 240 mi. He drove for 1 hr in city traffic and for 3 hr on the highway. If his average speed on the highway was 20 mph faster than his speed in the city, determine his average speed driving in the city and his average speed driving on the highway.

Concept 4 Solve Applications Involving Rate of Work Done

Example 4 Malcolm and Jamal have been offered $100 if they can clean out a garage in under 2 hours. Malcolm can clean the garage in 3 hours and Jamal can clean the garage in 5 hours. Working together, can they clean the garage in time to make $100?

Skill Practice 4 Sheldon and Penny were awarded a contract to paint 16 offices in the new math building at a university. Once all the preparation work is complete, Sheldon can paint an office in 30 min and Penny can paint an office in 45 min. How long would it take them to paint one office working together? How long would it take them to paint all 16 offices?

Concept 5 Solve Applications Involving Proportions

Example 5 (1 of 2) The Vitruvian Man is a famous pen and ink drawing by Leonardo da Vinci. In the text accompanying the drawing, Leonardo lists proportions for the human body based on the work of the Roman architect Vitruvius.

Example 5 (2 of 2) The length of the outspread arms is equal to the height of a man. The maximum width of the shoulders is a quarter of the height of a man. The foot is one-seventh the height of a man. In modern terms, we would write. The ratio of the length of outspread arms to height is 1:1. The ratio of shoulder width to height is 1:4. The ratio of the length of one foot to height is 1:7. The length of Zelda's foot is 54 inches less than her height. If she conforms to Leonardo's ratios for a "man," what should be her height?

Skill Practice 5 For the 104th Congress, there were 4 more Republicans than Democratic in the U.S. Senate. This resulted in a ratio of 13 Republicans to 12 Democrats. How many senators were Republicans and how many were Democrat?

Geometry Application Example 6 In his hallway, Robert has an old rectangular throw rug measuring 2 feet by 3 feet. After spending the weekend watching home improvement shows, he decides to upgrade the rug by adding a new border of width x feet around the edge to increase the perimeter to 14 feet. Determine the value of x.