3.11 More Expressions and Equation

1. 3.11 More Expressions and Equation • Goals: To set up and solve word problems

2. Expressions • Goal: simplify by using one variable instead of 2 • How: substitute what the variable =

3. Ex 1: There are 9 fewer Math books than English books. Write an expression for the total number of books Way 1 (in terms of Math books) Way 2 (in terms of English books) M= Math books E= English books Total books= M +E M=E-9 Total books: (E-9) +E = 2E -9 M= Math books E= English books Total books = M+E E=M+9 Total books: M + (M+9) = 2M +9

4. Consecutive Integer Expressions • Consecutive integers are number one right after another • Example: 1,2,3,4… • Always start the first consecutive integer as “n”

5. If “n” is the first integer, write an algebraic expression for the “2nd consecutive integer.” n + 1 Write an algebraic expression for the “3rd consecutive integer.” n + 2 Write an algebraic expression for the sum of three consecutive integers. n + (n + 1) + (n + 2)

6. Consecutive Even or Odd Integers • Consecutive even integers example: 2,4,6,8,10….. • Consecutive odd integers example: 1,3,5,7,9… • Consecutive even and odd integers have the same formula

7. Write an algebraic expression for the “2nd consecutive even/odd integer.” n + 2 Write an algebraic expression for the “3rd consecutive even/odd integer.” n + 4 Write an algebraic expression for the sum of three consecutive even/odd integers. n + (n + 2) + (n + 4)

8. Example 2: Write an expression for the sum of an even integer, ½ of the next even integer, and 3 times the following even integer First even integer = n Next even integer = n+2 Following even integer= n+4 n + ½(n+2) + 3(n+4) = 9/2n +13

9. Equations • Set the consecutive integers = to the sum ex of 3 consecutive integers: n + (n+1) + (n+2) = sum • Set the consecutive odd/even integers = to the sum Ex of 3 consecutive even/odd integers: n + (n+2)+ (n+4) = sum

10. Ex 3: Find three consecutive integers whose sum is 90. Let n = first integer n + (n + 1) + (n + 2) = 90 3n + 3 = 90 3n = 87 n = 29 29, 30, and 31

11. Ex 4: Find three consecutive even integers whose sum is 42. Let n = first integer n + (n + 2) + (n + 4) = 42 3n + 6 = 42 3n = 36 n = 12 12, 14, and 16

12. Ex 5: The sum of an integer and three times the next consecutive integer is 51.What is the largest number? Let n = first integer n + 3(n + 1) = 51 4n + 3 = 51 4n = 48 13 n = 12

13. Ex 6: The perimeter of a rectangle is 150 cm. The length is 15 cm greater than the width. Find the dimensions • P = 2L + 2W • P=150 • 150 = 2L +2W • L=(W +15) • 150 = 2 (W +15) +2W • 150 = 2W + 30 +2W • 150= 4W +30 • 120 =4W • W=30 cm • L=30 +15 = 45 cm

14. Homework: Page 160 (2-22, even, 27 and 36) write down the main information from the word problem: