I have a story problem.

Question

A badminton racket costs 4/5 the cost of a tennis racket. The tennis racket costs $7.60 more than the badminton racket. what is the cost of the badminton racket?

Answer 1

Let b be the cost of the badminton racket 
      t be the cost of the tennis racket.
 
   b = 4/5 t             [eq1]
   t = $7.60 + b      [eq2]

 

from (eq1):

   t = (5/4)b

 

substitute into (eq2):     [note: substitute for variable you want to eliminate]

   (5/4)b = $7.60 + b

    (1/4)b = $7.60         [subtract b from both sides]

      b = $30.40

The price of the badminton racket is $30.40

Answer 2

Let b be the cost of the badminton racket 

      t be the cost of the tennis racket.

 

   b = 4/5 t

   t = $7.60 + b

 

using substitution,

 

   t = $7.60 + 4/5 t

t - 4/5 t = $7.60 + 4/5 t - 4/5 t

1/5 t = $7.60

 

multiply both sides of the equation by 5.

 

     5 (1/5 t) = (5)($7.60)

 

           t = $38.00

 

The tennis racket costs $38.

 

To solve for the cost of the badminton racket, solve for b in terms of t.

 

     b = 4/5 t

     b = 4/5 (38)

  

     b = $30.40

 

then, the badminton racket costs $30.40

 

Hope that helps.