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1.2 Variables , Expressions, and Equations

1.2 Variables , Expressions, and Equations. Objectives : Use variables to represent unknown quantities. Represent real-world situations with equations and solve by guess-and-check .

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1.2 Variables , Expressions, and Equations

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  1. 1.2 Variables, Expressions, and Equations Objectives: Use variables to represent unknown quantities. Represent real-world situations with equations and solve by guess-and-check. Standards Addressed: 2.5.8.A: Invent, select, use and justify the appropriate methods, materials and strategies to solve problems.2.8.8.G: Represent relationships with tables and graphs in the coordinate plane and verbal or symbolic rules.

  2. Using variables and expressions to form equations provides a systematic way of representing and solving many types of problems. • Variablesare letters that are used to represent quantities in algebra. • An algebraic expression is formed by combining numbers and variables using operations of addition, subtraction, multiplication, division, powers, and roots.

  3. Writing in Math: You can translate many words for operations into symbols. • Total/More Than/Increased By ADDITION • Difference/Fewer Than/Less Than/Decreased By SUBTRACTION • Product/Times MULTIPLICATION • Quotient/Divided By DIVISION

  4. Ex. 1 Write a variable expression for each word phrase. • a. nine more than a # y 9 + y • b. 4 less than a # n n – 4 • c. a # z times three 3z • d. A # n divided by 12 n ÷ 12 • e. 4 fewer than j j – 4 • f. the product of c and 3 3c • g. a # n increased by 5 n + 5 • h. 5 times the quantity 4 plus a # c 5(4 + c)

  5. Ex. 2A • Suppose that a rental shop charges an $8 fee plus $3 per hour to rent a bike. Make a table to show the value of the expression 8 + 3h when h is 6, 8, and 12 hours.

  6. Ex. 2B • Make a table to show the value of the expression 4m – 10 when m is 8, 9, 10, and 11.

  7. Ex. 3 AAt 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 write an equation that relates the expression to a total cost of $10. Expression: 4 + 2H Equation: 4 + 2H = 10

  8. EX. 3 BThe cost to rent a set of jet skis is a $20 fee plus $50 per hour. Make a table to show the total cost to rent the skis for 1 hour through 5 hours. Write an equation for the situation. Expression: 20 + 50H Equation: C = 20 + 50H

  9. When one side of an equation has the same value as the other side, the equation is true. • If the equation has a variable in it, you can substitute a value for the variable. • If the substitution gives you a true equation, then the value you substituted is a solution. • The solutions to an equation are all values that give a true equation when substituted.

  10. Ex. 4aJessica places 3 photos on the cover of her picture 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 of her photos? • 4P + 3 = 155 • Guess 1: p = 20 4(20) + 3 ≠ 155 83 is too small!! • Guess 2: p = 40 4(40) + 3 ≠ 155 163 is too LARGE!! • Guess 3: p = 38 4(38) + 3 = 155 CORRECT!!!!!

  11. Ex. 4BMegan places 2 photos on the cover of her picture 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 of her photos? • 5P + 2 = 67 • Guess 1: p = 10  5(10) + 2 ≠ 67 • Guess 2: p = 12  5(12) + 2 ≠ 62 • Guess 3: p = 13  5(13) + 2 = 62

  12. Ex. 5 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 equal to the area of Olympic National Park if 114,364 acres are destroyed each day worldwide? • a.Solve the problem by using the constant feature of a calculator. 922,654 – 114,364 = 808,290 693,926 579,562 465,198 350,834 236,470 122,106 7,742 * IT WILL TAKE 9 DAYS!! ** Calculator Keystrokes: 922,654 ENTER, Ans – 114,364 ENTER, ENTER

  13. b. Express the situation as an equation and use the equation to find the number of acres left at the end of the 3rd day. DAYS = D 922,654 – 114,364D 922,654 – 114,364(3) = 579,562

  14. Ex. 6 The Good family lives in a farmhouse that has a 1000-gallon water tank. On average, the family uses 80 gallons of water per day. Suppose that the tank is full. For how many days will the family have an adequate supply of water? • a.Solve the problem by using the constant feature of a calculator. 1000 – 80 = 920 840 760 680 600 520 440 360 280 200 120 40 * The Good Family has enough water for 12 DAYS!!

  15. b. Write an equation and solve it by using the table feature of a graphics calculator. G = 1000 – 80D D: # of days G = 1000 – 80D

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