1. College Algebra Chapter 1 Equations and Inequalities
Section 1.2
Applications with Linear and Rational Equations

2. Problem Solving Strategy
1. Read the problem carefully. Determine what the problem is asking for, and assign variables to the unknown quantities.
2. Make an appropriate figure or table if applicable. Label the given information and variables in the figure or table.
3. 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.
4. Solve the equation from Step 3.
5. Interpret the solution to the equation and check that it is reasonable in the context of the problem.

3. 1. Solve Applications Involving Simple Interest
2. Solve Applications Involving Mixtures
3. Solve Applications Involving Uniform Motion
4. Solve Applications Involving Rate of Work Done
5. Solve Applications Involving Proportions

4. 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.

5. Example 1 continued:

7. 1. Solve Applications Involving Simple Interest
2. Solve Applications Involving Mixtures
3. Solve Applications Involving Uniform Motion
4. Solve Applications Involving Rate of Work Done
5. Solve Applications Involving Proportions

8. 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

9. Example 2 continued: 10% trail mix 40% candy mix 12% party mix
10% trail mix
40% candy mix
12% party mix
amount of mix
pure fat

11. 1. Solve Applications Involving Simple Interest
2. Solve Applications Involving Mixtures
3. Solve Applications Involving Uniform Motion
4. Solve Applications Involving Rate of Work Done
5. Solve Applications Involving Proportions

12. 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

13. Example 3 continued:
Distance
Rate
Time
Daryl
Cynthia

15. 1. Solve Applications Involving Simple Interest
2. Solve Applications Involving Mixtures
3. Solve Applications Involving Uniform Motion
4. Solve Applications Involving Rate of Work Done
5. Solve Applications Involving Proportions

16. 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?

17. Example 4 continued:

19. 1. Solve Applications Involving Simple Interest
2. Solve Applications Involving Mixtures
3. Solve Applications Involving Uniform Motion
4. Solve Applications Involving Rate of Work Done
5. Solve Applications Involving Proportions

20. Example 5:
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.

21. Example 5 continued:
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.

22. Example 5 continued:
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?

24. Example 6: Geometry Application
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.