1. Applications of Linear Equations

2. Use percent in solving problems involving rates. Recall that percent means “per hundred.” Thus, percents are ratios in which the second number is always 100. For example, 50% represents the ratio 50 to 100 and 27% represents the ratio 27 to 100. PROBLEM-SOLVING HINT Percents are often used in problems involving mixing different concentrations of a substance or different interest rates. In each case, to get the amount of pure substance or the interest, we multiply. In an equation, percent is always written as a decimal. For example, 35% is written 0.35, not 35, and 7 % is written 0.07 not 7. Interest Problems (annual) principle × rate (%) = interest p × r = I Mixture Problems base × rate (%) = percentage b × r = p

3. EXAMPLE 1 What is the amount of pure acid in 40 L of a 16% acid solution? Find the annual interest if $5000 is invested at 4%. Using Percents to Find Percentages Solution:

4. PROBLEM-SOLVING HINT In the examples that follow, we use tables to organize the information in the problems. A table enables us to more easily set up an equation, which is usually the most difficult step.

5. EXAMPLE 2 Kg ofPercentageKg of Metal(as a decimal)Copper x0.40.4x 800.780(0.7)=56 x+800.50.5(x + 80) Solution: Let x = kg of 40% copper metal. Solving a Mixture Problem 160 kg of the 40% copper metal is needed. A certain metal is 40% copper. How many kilograms of this metal must be mixed with 80 kg of a metal that is 70% copper to get a metal that is 50% copper?

6. EXAMPLE 3 Amount InvestedRate ofInterest for in DollarsInterestOne Year x0.050.05x 2x + 30000.080.08(2x+3000) Solution: Let x = amount invested at 5%. $7000 was invested at 5% interest. With income earned by selling a patent, an engineer invests some money at 5% and $3000 more than twice as much at 8%. The total annual income from the investment is $1710. Find the amount invested at 5%.

7. Textbook Homework 2.1 1-71 ODD 2.2 1-75 ODD 2.3 5 - 53 ODD 2.4  5 – 65 ODD 2.5 5 – 85 EOO 2.6 3 – 67 EOO 2.7 7 – 53 EOO OR MYMATHLAB!