The document provides examples and step-by-step solutions to mathematical word problems involving functions, equations, and algebraic modeling. It includes 8 sample word problems, showing the work to determine an appropriate equation or function to model each problem and solve to find the unknown values. The overall goal is to help students analyze problems, determine solution strategies using algebra, and evaluate whether solutions make sense in context.

1. Mathematics Section 5, Content Standard 2, "Students analyze problems to determine an appropriate process for solution, and use algebraic notations to model or represent problems. (Algebraic and Analytic Thinking)“ Benchmark #4 "Analyze problems that can be modeled by functions, determine strategies for solving the problems and evaluate the adequacy of the solutions in the context of the problems."

2. Steps Examples Solutions Work Cited

3. Read the Problem Determine what you know and what you need to know. Write your variables Form an equation Solve the Equation

4. Example 1 Example 2 Example 3 Example 4 Example 5 Example 6 Example 7 Example 8 Solution 1 Solution 2 Solution 3 Solution 4 Solution 5 Solution 6 Solution7 Solution 8

5. A classroom contained an equal number of boys and girls. Eight girls left to play hockey, leaving twice as many boys as girls in the classroom. What was the original number of students present? Solution

6. Let the number of girls or boys = x 2(x-8) = x 2x - 16 = x x=16 There are 2x students in the class, therefore there are 32 students. Next Example Table of Contents

7. Flora had an average of 56% on her first 7 exams. What would she have to make on her eighth exam to obtain an average of 60% on 8 exams? Solution

8. Let x = the mark on the eighth exam. 56% = .56 (.56 * 7 + x)/8 = .60 3.92 + x = .60 * 8 3.92 + x = 4.80 x = 4.80-3.92 x = .88 = 88% Next Example Table of Contents

9. Bart goes to the corner store and buys an equal number of 35 cent and 30 cent candies for $22.75. How many candies did he buy? Solution

10. X = # OF 30 cent candy = # of 35 cent candy .30 x + .35 x = 22.75 x = 35 candies total # of candies = 2x = 70 Next Example Table of Contents

11. You are given this graph of a triangle DEF and you are asked its area. What do you think it is? Solution

12. a = 1/2bh b = 8 - 1 = 7 h = 5 - 1 = 4 a = 1/2(4*7) a = 1/2(28) a = 14 Units 2 Next Example Table of Contents

13. Fred picked four numbers out of a hat. The average of the four numbers is 9. If three of the numbers are 5, 9 and 12, then what is the fourth number? Solution

14. (x + 5 + 9 + 12) /4 = 9 (x + 26) /4 = 9 x + 26 = 36 x = 10 Next Example Table of Contents

15. I have sold 2/3 of my pencils for $0.15 each. If I have 8 pencils left, how much money did I collect for the pencils I sold? Solution

16. 1/3 * x = 8 x = 24 2/3 (24) = 16 16 * .15 = $2.40 Next Example Table of Contents

17. Darryl ate 100 peanut butter cups in five days. Each day he ate six more than he ate the previous day. How many peanut butter cups did Darryl eat on the first day? Solution

18. 100 in 5 days. x <- 1st day x+6 <- 2nd day x+12 <- 3rd day x+18 <- 4th day x+24 <- 5th day x + x+6 + x+12 + x+18 + x+24 = 100 5x + 60 = 100 5x = 40 x = 8 1st day he ate 8 Next Example Table of Contents

19. Two girls agree to go on a road trip together. They travel (x + 5)km on the first day. On the second day they travel 2km more than half of the distance they travelled on the first day. On the third day they drove 3 times as far as they did on the second day. If they drove 5000km total, find the value of x. Solution

20. (x+5)+1/2(x+5)+2+3[1/2(x+5)+2] = 5000 x+5 + 1/2x + 45 + 3/2x + 7.5 + 6 = 5000 3x + 23 = 5000 x = 5000-23/3 x= 1659 Table of Contents

21. All problems and solutions were obtained from the following website: Word Problems for Kids . 1999. 15 November 2008 < http://www.stfx.ca/special/mathproblems/>