Andy had a number of apples. He gave 1/3 of them to Cheryl and 1/4 of them to Ken. If he has 35 apples left, how many did he start with?

Question

Andy had a number of apples. He gave 1/3 of them to Cheryl and 1/4 of them to Ken. If he has 35 apples left, how many did he start with?

Answer 1

The key to solving this problem is to correctly translate the words and phrases of the problem into concise, precise math variables and expressions.  The math is actually easy.

 First, read and re-read the problem statement until you understand it and can put it into your own words.  How’s this:  “With a total value of x, there are three groups:  (1/3)x, (1/4)x and 35.  What is x?”  Do you agree that this is the problem?

 

Let x = starting number of apples

   [note: when possible, assign a variable to the value the

      problem asks you to find (so you won’t forget to solve for it later)]

 

     Starting number           (1/3) to Cheryl      (1/4) to Ken         left

               x                                 -   (1/3)x              - (1/4)x           =    35

 

The word “gave” means that we subtract that amount from what Andy has.  The word “left” means the result after Andy makes his gifts.

 

O.K., the easy math:

 

Re-write:

     x – (1/3)x – (1/4)x = 35  

        [to get rid of fractions, multiply by 12, the LCM of 3 and 4]

    12x – 4x – 3x = 420

            5x = 420                         [collect terms]

              x = 84                  [divide both sides by 5]

 

Checking (very important):

  Is   84  - (1/3)84 -  (1/4)84 = 35   ?

        84 - 28  -21 = 35   ?

              35 = 35   ?yes