One integer is 4 more than another. Their product is 32. Find the integers.

Question

I suck at word problems. 

Explain please with simple explanation 

Answer 1

Suppose that you were not familiar with algebra.  One integer is 4 more than another.  This is where you add & subtract. You know the product of these integers is 32.  So we pick all factored pairs that give a product of 32.

 

1 × 32 = 32

2 × 16 = 32

4 × 8 = 32

 

 

Each of these pairs give a product of 32.  All we need to do is find the pair that gives a difference between the factors.  4 and 8 works.

Answer 2

The key to word (story) problems is to learn to translate the words and phrases into concise, precise math expressions -- with variables and operations.
 
First, let A be the one integer and B be the other integer.
 
Now, translate:
     "One integer is 4 more than another"    means that     A = 4 + B     (eq1)
     "Their product is 32"         means      A*B=32      (eq2)
     "Find the integers"         means       report A, B
 
O.K., now the math is easy:
      Put 4+B [from eq1] in place of A in eq2:
            (4 + B)*B = 32
             4B + B*B = 32     (distribute the B)

            B*B + 4B - 32 = 0       (subtract 32 from both sides)

           (B + 8)(B - 4) = 0          (factor the equation or use quadratic formula)

              B = -8   or B = 4         (note: both -8 and 4 are acceptable integers)

              A = -4   or A = 8         ( and A*B is indeed 32)

 

          A = -4 and B = -8

     or  A = 8 and B = 4 
 

Answer 3

step 1:  divide the # 32 by 2.

 

step 2:  start taking away one number above and below until you have a sum of the two numbers that reads 32.

 

Viz:  32 by 2 = 16.

 

        If 16 + 16 = 32, then try 17 + 15, or 18 = 14, or 19 + 13.  Any of the numbers will add up correctly.