Algebra II Emporium
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This page is designed to help anyone who has any trouble with Algebra II, to just brush up on what they already know, or to learn how Algebra II works.
The Atlantic City Fabrics Company makes clothes for many people across the country. They are well known for their white and grey sweaters. The white sweaters are sold for $4.95 each. Whereas the black ones sell for $7.95. In a month, they sell 40 sweaters. Their total intake, is $282.00. How many of each type of sweat shirt did they sell? 

Procedure: We have a total of 40 sweaters, W white ones, and B blacks ones. So we could use that to infer that W+B=40. Then to get out second equation we know that each white sweater costs 4.95, and that each black one costs 7.95; so therefore 4.95w+7.95b= $282.00 
 

 W+B=40                                           
4.95w+4.95b=$282.00  
W=-b+40  

4.95 (-b+40) +7.95= $282.00 
-4.95 + 198 +  7.95p=$282.00 
-4.95                 -4.95 
3b + 198=$282                             
-198         -198 ;                            
3b=84 
84/3=28 

W + 28 = 40 
-28 -28 
W = 12 

W=12
B=28
 
 
 
 
SMILE YOU JUST DID YOUR FIRST EQUATION!!!!
 
Now we will solve an algebraic problem concerning substitution. The following equations were given to us: 

3x + 2y=10 and X=3y + 10. We will then take these equations to find out what both x and y equal 

Procedure: We were given the two equations, so there is no need to ask where we got them from. In this case we know what x means 3y + 10. So then we would take that equation, and plug it into the equation 3x + 2y =10. They you would end up becoming 3(3y + 10) + 2y=10. Now you would distribute, ending up with 9y + 30 + 2y=10. Then combine the y's, 11y + 30 = 10. Then you would subtract thirty, ending up with 11y= -22. This problem is already long " finished", but you would then divide by eleven, arriving at y=-2. Then plug -2 back into the 3x + 2y=10 equation. Finally you would get x=4 and y=-2.

 3x+2y=10 and X=3y+10  
3(3y+10) + 2y=10                         
9y + 30 + 2y=10                            
+ 2y +2y  
11y + 30= 10                                   
-30        -30  
11y= -22  
/11    /11 
y= -2  

3x + 2y=8 
3x + 2(-2)=8            
3x + -4=8 
- -4    - -4 
3x = 12 
/3      /3 
X = 4 

  X=4 
 Y=-2
 YOU SKATED RIGHT THROUGH THAT ONE!!!
GREAT JOB!!!
  HOW ABOUT ANOTHER?
 
 

 

Now for the last and final problem. After this one I'll leave you alone....   

Procedure: This problem is a linear combination problem. We start off with 5x + 6y = -11, and 3x + y = - 4. In order to solve this equation we need to cancel out one of the variables, in this equation, we have only one variable who is "vulnerable." Its the y in the 3x + y = - 4. In the other equation we have positive 6y so in order for us to cancel the other y we need a -6. So multiply that y by -6 so now we'll have -18x + -6y = 24. Now we can cancel the Y's out and we can combine the x's. We're left with   -13 x = 13. Then we divide by 13, and determine that X = - 1. Then plug that back into the equation to get Y.

 5x + 6y = - 11 and 3x + y = - 4  
                                                                    
(-6) 3x + y = - 4  -18x + -6y = 24                 
                                                                       
5x + -18x = -13x and -11 + 24= 13                   
                                                                         
-13x = 13 
13/-13 = -1 
X= - 1 
5 (-1) + 6y = -11 
-5 + 6y = -11 
 + 5      + 5 
6y = - 6 
-6/6 
Y = - 1 
               X= -1 Y = - 1
 
You blew through them all, now you can say "I CAN DO ALGEBRA II" (corny huh?)
Here's another math page, it has helpful notes                                           Math Page 
Here's a page that has nothing to do with math, but it's a cool game          Cyberstrike 2 
 
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