Ok.. It says to solve for base, round to nearest cent!!

Question

Original + Increase = New value

(Base).                           (Part).  

 

I'm guessing that 800 is Part(after increase) an rate of increase is 25%. How do I find the base??

 

Base + 25% = 800 (New Value)

That's my problem!!!

 

Example problem is: 

                     /        10% increase  /

                     /                                 /

110% (rate) /                               / =203,500

                     /                                /

                    / 100% original base. /

 

 

The $203,500 is (part=increase+increase)

 

Says to use formula to solve for base in increase problems: 

Original + Increase = New Value

 100%.          10%.             110%

 

Substitute % with part = $203,500 an rate = 110% which is:

 $203,500=B x 110%

 

Solving for B is : 

           $203,500                  $203,500

  B=   -------------------       B= -----------------

            110%                           1.1

 

  B= $185,000

 

So value is $185,000

                                              $185,000

                                            +    18,500

                                           ---------------------

                                             $203,500

 

$203,500 is 110% of $185,000.

 

I do not understand any of that an still have no idea how I'm supposed to figure out:

Part.             Increase.             Base.     

$800                25%.                    ? 

Answer 1

To understand how to work these kinds of problems, first, you need to understand that percentages are not amounts, they are ratios or fractions that must be multiplied by a quantity to get another quantity.  The $800 is a quantity, and the base you are looking for is a quantity, but 25% is not a quantity and can not be added or subtracted from dollar amounts.

Second, you need to understand that the base is considered to be 100% of itself--that it why this quantity is called the base.  All other ratios(percentages) are "based" on this amount.  Therefore, an increase of 25% means that you add 25% of the base to 100% of the base.  This makes 125% of the base, or the base (B) times 1.25.  Since you multiply the base times 125% to get the new amount, if you are given the new amount and need to find the base, you have to divide the new amount by 1.25. Your equation should actually be B(100% +25%) =$800, which then becomes B(125%)=$800 or B(1.25) = $800 and finally, B= $800/1.25.  I hope this helps.

Answer 2

Let x = the base

 

If x + 25% of the base = 800, then x + 0.25x = 800

 

                                                        1.25x = 800

 

                                                              x = 800/1.25

 

                                                                 = 640