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Chris puts one tenth of each paycheck into savings. Her current paycheck is $200. She decides to also put into savings, any amount she earns over $200. The expression below represents the percent of her paycheck that Chris saves when she makes x dollars more than her current paycheck.

100(x+20)x+200

Drag and drop the expressions into the boxes to identify their meaning.

 

Simplify. Enter your answer in the box.

oscar.a1551  Nov 14, 2018
 #1
avatar+92785 
+2

First one

 

Original ratio of saved to total money per paycheck  =   20 / 200

 

Final ratio of saved to total money per paycheck   =  (x + 20) / (x + 200)

 

Final amount saved per paycheck   =   x + 20

 

 

cool cool cool

CPhill  Nov 14, 2018
 #2
avatar+92785 
+2

Second one

 

Note that what we really have is just this

 

4x                       6x

_____   รท        ______

5 + x                  x + 2

 

So.....just like "normal" fractions....we just invert the second and multiply

 

4x                       x + 2

_____    x         ______     =

5 + x                    6x

 

 

4x               x + 2

__      x      _____

6x               x + 5

 

 

4               x + 2

_      x       ____

6               x + 5

 

 

2            x + 2

__     x   ____

3            x + 5

 

2x + 4

_____

3x + 15

 

 

cool cool cool

CPhill  Nov 14, 2018
 #3
avatar+92785 
+2

Last one

 

Factor  x^2 + 4x + 3   =  (x + 3) ( x + 1)

Factor   x^2+ x  =   x ( x + 1)

Factor  2x^2 -3x + 1  =   (2x - 1) (x - 1)

 

So......just like the last one.....we really have

 

 

( x + 3) ( x + 1)              (2x - 1) ( x - 1)

____________      x     ______________

   2x   -  1                        x  ( x + 1)

 

"Cancel"   the  ( x + 1)   and  2x - 1  factors    and we have

 

 

( x + 3) ( x - 1)

___________

         x

 

 

 

cool cool cool

CPhill  Nov 14, 2018

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