1. SECTION 8.5-8.6 Solving Rational Equations and their Applications Solving equations containing fractions: Key: GET RID OF THE FRACTIONS! Solve: 3 4 2

2. When solving proportions (1 rational expression set equal to another), then just cross-multiply.

3. Applications of proportions: Rates: A ratio of two numbers (usually in different units), where one number depends on the other in some manner. When setting up a proportion (one ratio = another ratio), make sure the units of the numerators match and the ratios of the denominators match. The monthly loan payment for car is $29.50 for each $1000 borrowed. At this rate, find the monthly payment for a $9000 loan. The phrase “for each” is like “per” in a rate. Since it is $29.50 “for each” $1000 borrowed, the rate is written:

4. Example: An investment of $1200 earns $96 each year At the same rate, How much additional money must be invested to earn $128 each year? What are we asked to find? How much ADDITONAL money must be invested in order to earn $128 each year. Let x = additional money to be invested. Given info: Rate of investment = Investment/Amount Earned = Also, amount earned from new investment is $128.

5. Work Problems Savannah can paint a room in seven hours. Jordan can paint the same room in nine hours. How long does it take for both Savannah and Jordan to paint the room if they are working together? Rate of Work * Time Worked = Part of Job Completed Rate of Work is the portion of a job that can get done in 1 unit of time (usually hours). If Savannah can paint a room in seven hours, then her rate of work is 1/7 = 1 job/7 hours = 1/7 of a job in 1 hour. Jordan’s rate of work = 1 room/9 hours = 1/9 Savannah’s Part + Jordan’s Part = Whole Job = 1 What are we being asked to find? How long it takes for both Savannah and Jordan to paint the room working together. That is, TIME. Let t = time to work together.

6. Megan and Julia can finish a piece of work in 15 days. Megan can do the job herself in twenty days. If Julia wanted to do the job alone, how long would it take her? In this case, let t = time for Julia to do the job alone. Julia’s rate of work = Given information. The whole job can get done in 15 days. Megan’s rate of work is ____ Megan’s Part + Julia’s Part job = 1 Megan’s Rate of Work xTime Worked Together +Julia’s Rate of Work xTime Worked Together = 1