Word+Problems

**  Welcome to the world of Word Problems! We hope to teach you as much everything we can to help you understand word problems! =D **

Definiton of **WORD PROBLEM** = the term word problem is often used to refer to any mathematical exercise where significant background information on the problem is presented as text rather than in mathematical notation. (google)

All you need to do to solve word problems is look at them in different ways until you find the way that works best for you.Through out this page we will show you different things to look for in word problems to help you understand and solve them. 

[|guess format.ppt]


 * __*Tips*__**
 * Remember to use BEDMAS (Brackets, Equations, Divide, Multiply, Add, Subtract)
 * Fractions are the same a dividing
 * fractions = decimals = percents

**Example 1: From Words To Math** 1. Triple a number = 3n 2. 50 more than a number = n+50 3. 25 increased by a number = 25+n 4. a number decreased by 5 = n-5 5. 15 less than a number = 15-n 6. half a number = n /2 7. a number over 10 = n/10 8. 12 over a number = 12/n 8. 12 over a number = 12/n 

    Isolating variables may seem confusing at first but once you know the basics, it really is a breeze! Keep in mind that the word isolate means to set apart, or separate.  
 * Example 2: Isolating Varibles **

a) To isolate "Z" we have to subtract both sides by 4.

Z+4 = 12 Z+4**-4** = 12**-4** Z = 8

Answer: **Z = 4**

b) To isolate "H" we have to divide both sides by 3.

H(3) = 21 H(3) /3 = 21/3 H = 7

Answer: H = 7 <span style="font-size: 115%; font-family: Tahoma,Geneva,sans-serif;">

**<span style="font-size: 105%; color: rgb(126,84,187);">Example 3: Dividing Word Problems ** <span style="font-size: 126.78%; font-family: Tahoma,Geneva,sans-serif;">When you are solving for an unknown sometimes you need to divide. If you have 5n and you want to find just "n" you need to divide by 5.

a)2 numbers added together equal 41. Find the two numbers.


 * G-**total 41

<span style="font-size: 115%; font-family: Tahoma,Geneva,sans-serif;"> <span style="font-size: 126.78%; font-family: Tahoma,Geneva,sans-serif;">**U-**the two numbers. Let n= the first number Let n + 1= the second number. n+ n + 1= 41

<span style="font-size: 115%; font-family: Tahoma,Geneva,sans-serif;">**E-** 2n + 1 = 41 <span style="font-size: 126.78%; font-family: Tahoma,Geneva,sans-serif;">2n =41-1 2n/2 = 40/2 <span style="font-size: 133.12%; font-family: Tahoma,Geneva,sans-serif;"> n = 20

n+1 =(20)+1 =21 <span style="font-size: 126.78%; font-family: Tahoma,Geneva,sans-serif;"> <span style="display: block; font-size: 120.75%; font-family: Tahoma,Geneva,sans-serif; text-align: left;"> <span style="font-size: 115%; font-family: Tahoma,Geneva,sans-serif;">
 * S**- n=20
 * S**- Therefore n = 20 so the first number equals 20, and the second number equals 21.

<span style="display: block; font-size: 120.75%; color: rgb(98,167,213); font-family: Tahoma,Geneva,sans-serif; text-align: left;"> <span style="font-size: 156%; color: rgb(255,166,0);">Example 4: Making words from an Equation This can either be really simple or really hard depending on the way you look at it.

First you solve the equation given. 5n+3 = 33 5n+3-3 = 33-3 5n = 30 5n /5 = 30/5 n = 6

Now you make up anything that you think will work with this equation.

5n+3 = 33 n = 6

Marissa went apple picking. she Started with 5 apples. After 20min of apple picking her brother comes with 3 more. H ow many apples did she pick in 20 min?

__**<span style="color: rgb(189,0,255);"> <span style="font-size: 130%; color: rgb(189,0,255);">Review. **__

(All questions from Mathpower 9) 1. Eight more than a number is twenty. 2. A number multiplied by six is seventy-two, 3. Hadib is eight years older than Cam. The sum of their ages is twenty-four. 4. Karl has three times as many stamps as Tim. Together they have 2400 stamps. 5. A hot water tank holds 200L of water. When the tap is opened, the water drains at a rate of 15mL/min. The amount of water left in the tank after t minutes is given by A= 200 - 15t. How much water will be in the tank after 5 min? 10 min? 6. The formula for the area of a rectangle is A = lw. Solve for w. 7. Shandra is a math tutor. She charges $20 a visit plus $25/h. a)Write a formula that determines her earnings from the hours she tutors on a visit. b)How much wil she earn if she tutors for 3h? 8. Sally has twice as many dimes as nickels. The total value is $3.50. How many nickels does she have?

**__<span style="color: rgb(229,87,87);">Solutions: __** __**1**__. 8 + x = 20


 * __2__**. 6x = 72

x + x + 8 = 24 2x = 24 - 8 __2x__ = __16__ 2 2 x = 8 (8 + 8= 16) Therefore, Cam is 8 years old and Hadib is 16 years old.
 * __3__**. Let x = Cams age. Let x + 8 = Hadibs age.

__**4**__. Let x = the amount of stamps Tim has. Let 3x = the amount of stamps Karl has. 3x + x = 2400 __4x__ = __2400__ 4 4 <span style="font-size: 138%; font-family: Tahoma,Geneva,sans-serif;"> x = 600 (3(600) = 1800) Therefore, Tim has 600 stamps and Karl has 1800.

= 200 - 15(5) = 200 - 75 = 125L Therefore after 5 minutes of the tank draining there would be 125L of water left. A = 200 -15t = 200 - 15(10) = 200 - 150 = 50L Therefore after 10 minutes there would be 50L of water left in the tank.
 * __5__**. A = 200 -15t

__A__ = __lw__ l l __A__ = w l
 * __6__**. A=lw

b) y = 25h + 20 =25(3) + 20 =75 +20 =95
 * __7__**. Equation a) y = 25h + 20

Therefore after 3 hours of tutoring she will earn 95 dollars. Let 2x = # of dimes. 0.10(2x) + 0.05(x) = $3.50 0.2x + 0.05 = $3.50 __0.25x__ = __$3.50__ 0.25 = 0.25 x = 14 (2(14) = 28) Therefore Sally has 14 nickels and 28 dimes.
 * __8__**. Let x = # of nickels.

<span style="display: block; font-size: 115%; font-family: Tahoma,Geneva,sans-serif; text-align: left;">So remember the hardest thing about word problems is to get the needed information from the question. Once you have all the correct information and the equation, you just need to solve the equation (__only__ if asked).

<span style="font-size: 115%; font-family: Tahoma,Geneva,sans-serif;">

<span style="display: block; font-size: 115%; font-family: Tahoma,Geneva,sans-serif; text-align: left;">By: Brianne, Crystal, Evan, Marjorie, and Francesca. __**Citations:**__ "Either you do or you don’t!." __Special 2 Me__. 28 Sep.. 17 Dec. 2008 < <span style="display: block; font-size: 115%; color: rgb(42,0,255); font-family: Tahoma,Geneva,sans-serif; text-align: left;">http://images.google.ca/imgres?imgurl=http://specialedandme.files.wordpress.com/2007/08/questionmarks.jpg&imgrefurl=http://specialedandme.wordpress.com/2007/09/28/either-you-do-or-you-dont/&usg=__GZZ__////__>__// <span style="display: block; font-size: 115%; font-family: Tahoma,Geneva,sans-serif; text-align: left;">

//__<span style="font-size: 115%; font-family: Tahoma,Geneva,sans-serif;">Knill, G. (1999). __//__Math Power 9 Ontario Edition//. Toronto: McGraw-Hill Ryerson.//

Confused//. (2007). [On-line photograph]. Retrieved December 13, 2008, from//__ <span style="font-size: 115%; font-family: Tahoma,Geneva,sans-serif;"> //<span style="color: rgb(0,13,255);">http://jamin.org/blog/wp-content/uploads/2007/11/confused.org //

__Coolclips- Apples//. (n.d.). [On-line photograph]. Retrieved December 18, 2008, from__ <span style="color: rgb(18,17,232);">http://previews2.nvtech.com/100/tf05038/NVTech_food0434.jpg __