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3.1 Writing Equations

3.1 Writing Equations. WARM UP. Write the following verbal expressions as algebraic expressions: 1) The difference of twice a number x and 4. 2) 3 times a number y less than twice the sum of a number x and 5 Write the following algebraic expressions as a verbal expression.

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3.1 Writing Equations

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  1. 3.1 Writing Equations

  2. WARM UP Write the following verbal expressions as algebraic expressions: 1) The difference of twice a number x and 4. 2) 3 times a number y less than twice the sum of a number x and 5 Write the following algebraic expressions as a verbal expression. 3)3 + 4n 4) 5 (x + 1) – 12

  3. What is the difference between writing an algebraic expression and writing an equation? • Requires having equality in an equation or equals sign to say two expressions are the same • Equations have = signs • Expressions do not (2 expressions can become an equation)

  4. Translate each sentence into an equation. 1)Five times the number a is equal to three time the sum of b and c. 2)Nine times y subtracted from 95 equals 37. 3)The product of five and the sum of m and n is the same as seven times n. 4)Two times a number t decreased by 8 is identical to seventy. 5a = 3(b+c) 95 – 9y = 37 5(m + n) = 7n 2t – 8 = 70

  5. Four-Step Problem Solving Plan EXAMPLE: Today, 2,000,000 gallons of ice cream are produced in the United States each day. How many days can 40,000,000 gallons of ice cream be produced in the United States? • STEP 1: EXPLORE THE PROBLEM STEP 2: PLAN THE SOLUTION • Read the problem carefully • Identify what information is given • Identify what you are asked to find • Choose a strategy to solve the problem • STRATEGY #1: Write an Equation: • Define a Variable:choose a variable (letter) to represent unknown numbers in the problem Know: 2,000,000 gallons of ice cream are produced in US each day. Want to Know: how many days it will take to produce 40,000,000 gallons of ice cream Let d represent the number of days needed to produce the ice cream. 2,000,000 * d = 40,000,000

  6. STEP 3: SOLVE THE PROBLEM • STEP 4 EXAMINE THE SOLUTION • Use the strategy from Step 2 to solve the problem • Check your solution in relation to the original problem • Does it make sense? • Does it fit the information in the problem? “What number of times 2,000,000 = 40,000,000?” 2,000,000d = 40,000,000 d = 20 20 days makes sense

  7. Formulas • specific type of equation that states a rule for the relationship between certain quantities • For formulas it’s important to identify all the variables. • You are defining a variable • Using known quantities with formulas we can plug them in to find others

  8. Translate each sentence into a formula: 1)The area of a triangle is equal to one half times the base times the height. • a.What is the area of a triangle with base 4 and height 11? 2)The perimeter of a rectangle equals two times the length plus two times the width. • a.What is the perimeter of a rectangle with base 5 and height 7? A = ½ bh A = 22 P = 2l + 2w P = 24

  9. Practice 3)The volume of a rectangular prism (box) is the same as the product of the length, the width, and the height. • a.What is the volume of a triangle with length 4, width 3 and height 5? 4) The volume V of a sphere is four-thirds times  times the radius r of the sphere cubed. • a.What is the volume of a sphere with radius of 4? V = lwh V = 60 V = 4/3  r3 V =85.33

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