Story Problems

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/>