The price of item A is %20 less then the price of the item B. If it cost $45 for both items A and B find the price of each item.

Question

I need help on this word problem. I don't know how to set up an equation for this word problem. 

Answer 1

Percent may be written as 20% or 20/100 (=1/5) or 0.20 as needed by the problem.

The word "of" in a word (story) problem usually means multiply.

"Less than" says that we will subtract.

$45 "total" (implied) means we add.

"is" means equals

 

Let x = price of item A

     y = price of item B

 

Translate:

  "price of item A is %20 less then the price of the item B"

                 x       =        y    -   (20/100)y

 

  "cost $45 for both items A and B"    means

          $45          =         x   +   y

 

Math:

  [note: teachers and tutors have done this so often they skip steps here]

 

   100x = 100y - 20y    [multiply first equation by 100 to get rid of fraction]

   100x = 80y

 

     $45 - y = x             [from second equation]

 

Substitute for x:

    100($45-y)  = 80y

     $4500 - 100y = 80y             [distribute]

     $4500 = 180y            [add 100y to both sides]

         $25 = y                  [divide both sides by 180]

Plug in to second equation:

           $45 = x + $25

           $20 = x             [subtract $25 from both sides]

 

Checking (very important):

  Is $20 (price of A) 20% less than $25 (price of B)   ?

                $20   =  $25 - (20/100)($25)   ?

                $20 = $25 - (1/5)($25)   ?

                $20 = $25 - $5   ?

                $20 = $20   ?yes

 

   Is $20 + $25 = $45   ?

             $45 = $45   ?yes