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3.4 Expressions and Equations Goal: To translate phrases to algebraic expressions (emphasizing grouping symbols) To solve problems by writing and solving equations Technique • Underline key phrases and write what they mean underneath • Then put it all together going left to right Review of Key Words: Addition Subtraction Multiplication Division Review: Write an expression that means: 5 more than a number “n” n+5 Review: Write an expression that means: 9 less than a number “n” 9n n 9 New Stuff for Translating Expressions: • • • • • • Words that means a grouping symbol: “the sum of” “the difference of” “the quantity of” “the product of” “the quotient of” Example 1: 5 times the sum of a number and 5 5(n + 5) Example 2: 5 times the quantity 3 less than a number. 5(n – 3) Remember: with less than we write the expression backwards… NOT left to right. Example 3: 14 less than the product of 3 and a # (3n) - 14 Remember: with less than we write the expression backwards… NOT left to right. Example 4: 4 times the quantity 3 greater than a number 4(n + 3) Example 5: One-half the difference of a number and 1 1 n 1 2 Example 6: Two fewer than the product of 10 and a number 10n 2 Translating Equations • • • • • Read the problem a few times Underline key phrases Translate from English to Math symbols Set up your equation Solve c 21 = 2 Arthur is two years younger than Chan. Arthur is 21. How old is Chan? Example 1: Let c = the age of Chan. 21 = c - 2 23 = c Ex 2: = The number of salted peanuts in a nut mix is 13 times the number of cashews. There are 52 salted peanuts. How many cashews are there? Let c = number of cashews 52 = 13 • c 4=c Ex 3: Nora divided 315 cans equally among 26 cartons and had 3 cans left over. How many cans were in each carton? Let x = cans per carton (cans per carton)(# cartons) = total cans + 3 26x + 3 = 315 Ex 4: The final exam had three times as many points as the first test, plus a bonus question worth 25 points. The final exam was worth 160 points (including the bonus). How many points was the first test worth? Let x = points on first test Final = 3 times first test plus bonus 160 = 3x + 25 Ex 5: At Max's Restaurant the cost of a child's dinner is $3.00 less than the cost of an adult dinner. You bought four children's dinners and paid $18.00. Find the cost of an adult dinner. “x” Child dinner = x - 3 4 • Child dinner = $18 4(x – 3) = 18 Assignment: Page 133 # 1-16 , 22-26 all (1-12 write down the question, 13-16 and 22-26 write down what is most important from the question)