Variable, Expressions, and Equations

1. 1.2 Variable, Expressions, and Equations • Warm-up • NCSCOS / Objectives • Glossary Terms

2. 1.2 Variables, Expressions, and Equations Warm-up Evaluate each expression for x = 2, and x = 3 • 3x – 1, for x = 2 • 3x – 1, for x = 3 • 4(x + 3), for x = 2 • 4(x + 3), for x = 3 5 8 20 24

3. 1.2 Variables, Expressions, and Equations NCSCOS • 1.01, 1.02, 4.01 • Use variables to represent unknown quantities. • Represent real-world situations with equations and solve by guess-and-check. Objectives

4. 1.2 Variables, Expressions, and Equations Glossary Terms variable algebraic expression equation solution to an equation

5. 1.2 Variables, Expressions, and Equations Suppose that a rental shop charges an $8 fee plus $3 per hour to rent a bike. The amount charged for different times is shown in the following table: The pattern suggests, the bike rental cost $8 plus 3 times the number of hours h. So the expression could be rewritten with the variable for hours, h as 8 + 3(h) or 8 + 3h

6. 1.2 Variables, Expressions, and Equations Variables are letters that are used to represent quantities in algebra. For instance, with the example of the rental shop, the h was used to represent the number of hours the bike was rented. Algebraic expression are formed by combining numbers and variables. In the bike rental example, the cost of renting the bike can be shown as this algebraic expression: 8 + 3h

7. 1.2 Variables, Expressions, and Equations Ex 1: Make a table to show the value of the expression 8 + 3h, when h is 6, 8, and 12 hours. 8 + 3(8) 8 + 3(12) 8 + 3(6) 32 44 26 Ex 1a: Make a table to show the value of the expression 4m – 10, when m is 8, 9, 10 and 11. 4(9) – 10 4(10) – 10 4(11) – 10 4(8) - 10 26 34 22 30

8. 1.2 Variables, Expressions, and Equations Two algebraic expressions separated by an equal sign form an equation. The following example helps demonstrate expressions and equations. Ex 2: At City Park you can rent in-line skates and protective gear for $2 per hour plus a $4 fee. Write an expression that represents the cost of renting skates and then solve the equations.

9. 1.2 Variables, Expressions, and Equations Ex 2a: The cost to rent a set of jet skis is $50 per hour plus a $20 fee. Write an equation for the cost to rent jet skis and make a table to show the total cost to rent the skis for 1 hour through 5 hours. where: c = cost in dollars and h = number of hours c = 20 + 50(h)

10. 1.2 Variables, Expressions, and Equations Ex 2b: Write an equation to represent a problem situation. Membership in a gym at a community center costs $15 per month plus a one-time fee of $50. Write an equation for the total cost, c, for membership over m months. The cost is $50 plus $15 every month. c = 50 + 15m or c = 15m+ 50

11. 1.2 Variables, Expressions, and Equations Solutions to equations: When one side of an equation has the same value as the other side, the equations are said to be equal. 4 + 2(3) = 6 + 2(2) true or not true? 4 + 6 = 6 + 4 10 = 10 True

12. 1.2 Variables, Expressions, and Equations The solution to and equation are all values of the variables that give a true equation when substituted for the variables. In many equations, there is just one solution. Find out the solution to Jessica’s photos. Ex 3: Jessica places 3 photos on the cover of her photo album. She places 4 photos on each of the other pages. She has 155 photos in all, how many pages will she need if she uses all her photos? She needs 38 pages 3 + 4(p) = 155 4(p) = 152 p = 38

13. 1.2 Variables, Expressions, and Equations Ex 3a: What if Jessica still placed 3 photos on the cover of her photo album, and placed 4 photos on each of the other pages, but had 160 photos. How many pages would she need if she used all her photos? 3 + 4(p) = 160 Since she could not use a quarter page, she would need the next whole number, so she would need 40 pages. 4(p) = 157 p = 39.25

14. 1.2 Variables, Expressions, and Equations Ex 3b: Megan places 2 photos on the cover of her photo album. She places 5 photos on each of the other pages. She has 67 photos in all, how many pages will she need if she uses all her photos? She needs 13 pages 2 + 5(p) = 67 5(p) = 65 p = 13

15. 1.2 Variables, Expressions, and Equations Ex 3c: Marge’s class is going on a field trip to an aquarium. The class rate is $12 per student plus $25. How many students can go if the class has only $335 to spend. Only 25 students can go. 25 + 12(s) = 335 25 – 25 + 12(s) = 335 - 25 12(s) = 310 s = 25.83

16. 1.2 Variables, Expressions, and Equations Ex 4: In 1990, the United Nations reported a deforestation figure of around 114,364 acres of trees per day. The area of Olympic National Park is about 922,654 acres. How long would it take to lose an area of forest about the size of the Olympic National Park if 114,364 acres were destroyed each day worldwide? Let d represent days 922,654 = 114,364(d) 922,654 = 114,364(d) 114,364 114,364 About 8 days, would destroy 914,912 acres. 8.067 = d

17. 1.2 Variables, Expressions, and Equations Ex 4a: Using the same information of deforestation (around 114,364 acres of trees per day), how many acres would be destroy after three days? Let A represent acres and d represent days A = 922,654 – 114,364(3) A = 922,654 – 343,092 A = 579,562 There would be 579,562 acres left after the third day.