story problems

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."

Steps Examples Solutions

Work Cited

Read the Problem Determine what you know and what you need

to know. Write your variables Form an equation Solve the Equation

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

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

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

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

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%

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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

X = # OF 30 cent candy = # of 35 cent candy 

.30 x + .35 x = 22.75 x = 35 candies total # of candies = 2x = 70  

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

Solution

a = 1/2bhb = 8 - 1 = 7h = 5 - 1 = 4a = 1/2(4*7)a = 1/2(28)a = 14 Units2

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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

(x + 5 + 9 + 12) /4 = 9(x + 26) /4 = 9x + 26 = 36x = 10

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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

1/3 * x = 8x = 242/3 (24) = 1616 * .15 = $2.40

Next Example Table of Contents

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

100 in 5 days. x <- 1st dayx+6 <- 2nd dayx+12 <- 3rd dayx+18 <- 4th dayx+24 <- 5th day x + x+6 + x+12 + x+18 + x+24 = 1005x + 60 = 1005x = 40 x = 81st day he ate 8Next Example Table of Contents

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

(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

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All problems and solutions were obtained from the following website:

Word Problems for Kids. 1999. 15 November 2008 < http://www.stfx.ca/special/mathproblems/>