Beth and Edith share 1600 mL of syrup. Edith received 3/5 of the amount received by Beth minus 40 mL. How much did each receive?

Question

Beth (1600 + ? ) x ?/? =

Edith (1600 + ?) x ?/? - ? =

Answer 1

The most important thing to learn from word (story) problems is how to correctly translate from words and phrases into concise, precise math variables and operations.  Make a "translation dictionary" and add to it with each problem you do:

   is         means         =

   of                           *

  minus                      -

  . . .

 

Let:

    B = amount Beth received

    E = amount Edith received

 

Translate:

  "Beth and Edith share 1600 mL"    means

     B     +     E       =     1600

 

  "Edith received 3/5 of the amount received by Beth minus 40 mL"  means

      E        =       (3/5) *                           B              -        40

 

  "How much did each receive?"   means    report  B and E

 

The math:

  To use substitution method, use one equation to find the value of one variable in terms of the other variable, then plug that into the other equation.  Note that this solves for the second variable.

 

  Let solve for B using the first equation:

       B = 1600 - E

 

  Plug that into the second equation wherever B occurs to solve for E:

      E = (3/5)*(1600-E) - 40

      E = 960 - (3/5)E - 40

      E + (3/5)E = 960 - 40           [add (3/5)E to both sides]

      (8/5)E = 920                    [multiply both sides by (5/8)]

       E = 575

 

Now, plug the value of E into either equation to solve for B.  Let's use the first equation:

      B = 1600 - 575

      B = 1025

 

Checking (very important):

  Is   1025 + 575 = 1600   ?

           1600 = 1600   ?yes

  Is   575 = (3/5)(1025) - 40   ?

        575 = 615 - 40   ?

        575 = 575   ?yes

 

Now, for practice, start with (E=1600-B) and substitute for E in the second equation.  You should get the same answer.  Which method is easier?

  

 

Answer 2

B represents amount Beth got

(3/5)B - 40 represents the amount Edith got

 

B + 3B/5 - 40 = 1600

 

Can you take if from here?