Algebra II for Dummies!


 
    When dealing with a substitution problem you are given an equation and underneath you are also given a value for one of the variables. Here's an example: 2x = 4 
                                                    x = 2
This type of format will work for any type of substitution problem. In Algebra II you have the same thing except you are given a word problem and you have to use the given info to find out what your equation is, watch:		 Let's try another kind of substitution problem. 

One week a business sold 40 scarves. White ones cost $4.95, and the printed ones cost $7.95.In all $282 worth of scarves were sold. How many of each kind were sold? 
 

On this type of problem you have to make your own variables, so we'll make w= white,& p= printed. We know that the # of white ones an the # of printed ones equals 40.The way you write that is w + p = 40

We also know the individual price of both kinds, so you'd write $4.95w + $7.95p = $282 
O.K. inorder to make this just like the other problem you hane to get rid of the p. 
w + p= 40
    -p     -p
w = 40-p   now were back to the old problem where you just plug in the variable.
$4.95(40-p)+$7.95p= $282
198 - 4.95p + 7.95p= 282
198 + 3p = 282
-198           -198
          3p = 84
          -3     -3
                           p=28(now you plug in the p)
         w + 28 = 40
             -28      -28<
                   w=12
You're done!!!!!!!

 
The perimeter of a rectangle is 86cm. The length is 19cm greater than the width. Find the length and the width  The measure of one of two supplementary angles is 8 degrees more than three times the other, find the measure of the larger angle.
O.K., the first thing you have to do is remember that the perimeter of a rectangle is 2L+ 2w so first you would write 2L + 2w = 86. Next is the substitution part, L= 19+w. 
Now all you have to is substitute the value for L and work the problem. 2(19+w) +2w= 86.
              38 + 2w + 2w = 86
               38 + 4w = 86
              -38      p;       -38
                     4w = 48
                       4       4
                          w = 12
Now you place the value for w into the problem(you can place it into anyone of the problems above).
 L = 19 + 12
                    L = 31
And that's a wrap!!!!!!!!		 Here's another type of problem.
          The measure of one of two supplementary angles is 8 degrees more than 3 times the other, find the measure of the larger angle.
    EX:   X + Y = 180 degrees
             The X stands for the bigger of the two angles.
            X = 8 + 3Y 
       Substitute the value for X into the first problem then use that answer to find X.
        8 + 3Y + Y = 180 degrees
        8 + 4Y = 180 degrees
       -8             -8
              4Y = 172
              4        4
                             Y = 43
Now put that value into the first problem, and you'll be done.

               X + 43 = 180
                   -43      p; -43
                                          X= 137
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