Connections among Representatives

Horses and Birds Horses and Birds Marie’s family went to Kentucky for their vacation. While in Kentucky, Marie noticed there were many horse farms. To occupy her time while the family was touring the countryside one day, Marie kept a total of the number of legs on the horses and birds in each pasture. At the end of the day, Marie asked her sister Michelle how many horses and how many birds had Marie counted if she counted a total of 284 legs. Michelle was able to quickly calculate the number of horses and the number of birds. Marie asked Michelle how she was able to do this so quickly. Michelle simply stated, “I used patterns and math.” Develop a strategy to determine the number of horses and birds if Marie counted a total of 284 legs.

Horses and Birds Each horse has ________ legs Each bird has ________ legs h number of legs for horses b number of legs for birds What equation can we use to represent the number of legs for more than one horse or bird H * 4 = B*2= If we count 54 legs total our equation should be? 4h + 2b = 54 legs

Notes Variable: a symbol, usually a letter that represents one or more numbers. Any letter may be used as a variable Mathematical expression: consists of numbers, variables, and operations To evaluate a mathematical expression, substitute the given numeric value in for the variable and perform the given operation.

Examples The sum of a number and 10 The difference of a number and 21 The quotient of 48 and a number 48/n The product of 6 and a number 6n One forth of a number 1/4n

Evaluating Evaluate the variable expression 3x - 5y, if x = 7 and y = 4. Substitute 7 for x and 4 for y. Put substituted values in parentheses. 3(7) – 5(4) • Simplify the resulting expression using order of operations. 3(7) – 5(4) 21 – 5(4) 21 – 20 = 1

Evaluate the each expression below if a = 6.2 and b = (− 9). a. 8a 8(6.2) = 49.6 b. ab (6.2) (− 9) = (−55.8) c. b(a – 3) (−9)(6.2 – 3) = (−28.8) d. 6b2 6(−9)2 6(81) = 486

Example 1 An electrician charges $45 per hour, plus $50 for the service call. Let x represent the number of hours worked. Equation 45x + 50

Example 2 The number of freshmen is ¼ of the number of total students. Let x represent the number of freshmen and n is the total number of students. Equation n * ¼ = x ¼ is also equal to 0.25

Example 3 The number of hours, x, worked at $15 an hour is the total pay, y. Equation y = 15x

Your work! 1. 7(8 + 4) = 2. 6(x – 7) = 3. 3(4x – 5) = 4. 12(4y + 12) = 1. 7(8 + 4) = 2. 6(x – 7) = 3. 3(4x – 5) = 4. 12(4y + 12) = 5. 1/5(x – 35) =

Distributive Property: distributing something as you separate or break it into parts. The distributive property makes numbers easier to work with, you are distributing. 1. 4(y + 9) = 2. 3(x + 4) = 3. 2(x + 3) = 4. 4(y + 12) = 5. 4(n + 5) = 6. 2(2n – 6) = 7. 4(x + 14) = 8. 12(x + 4) = 9. 5(x + 3) = 10. 3(y + 13) = http://www.youtube.com/watch?v=EixCbmu8GiY

Word Problems 11. The students in Mrs. Lane's class are building balloon-powered cars for a Mathematics project. Each student needs a balloon that costs $0.05, a package of wheels for $1.00, and a car frame kit for $1.50. Which equation can be used to find y, the amount in dollars, spent by all of Mrs. Lane's students, as related to x, the number of students in Mrs. Lane's class? A. y = ($0.05 + $1.00 + $1.50) B. y = $2.55x C. y = $2.55 + x D. y = $3.00x

Word Problems 12. Which expression is equivalent to the sum of 3 times a number and 6? A 3x + 6 B 3(x + 6) C x(3+6) D 3 + 6x

Word Problem 13. Which of the following represents the algebraic expression 6 less than a number n? A 6 ÷ n B 6 – n C n – 6 D n + 6