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: AdditionSubtractionMultiplicationDivision

Review: Write an expression that means: 5 more than a number “n” n + 5

Write an expression that means: 9 less than a number “n” Review:

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

Example 6: Two fewer than the product of 10 and a number

Translating Equations Read the problem a few times Underline key phrases Translate from English to Math symbols Set up your equation Solve

Arthur is two years younger than Chan. Arthur is 21. How old is Chan? Let c = the age of Chan = c - 2 = 2 c 23 = c Example 1:

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 2:

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 26x + 3 = 315 (cans per carton)(# cartons) = total cans + 3 Ex 3:

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 4:

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 $ Find the cost of an adult dinner. “ x” Child dinner = x Child dinner = $18 4(x – 3) = 18 Ex 5:

Assignment: Page 133 # 1-16, all (1-12 write down the question, and write down what is most important from the question)