One integer is 8 less than another integer. The product of the lesser integer and -5 and 28 more than the greater integer. What are the integers?

Question

One integer is 8 less than another integer. The product of the lesser integer and -5 and 28 more than the greater integer. What are the integers?

Answer 1

 

Let       x = one integer (the lesser one)

Let x + 8 = the larger integer

 

The product of the lesser integer and -5 is -5x,  That product is 28 more than the greater integer.

We can construct the following equation:

 

    -5x = x+8 + 28

    -5x = x + 36

    -6x = 36

      x = -6

 

The smaller integer is -6.

Since the greater number is 8 more than the lesser one, -6 + 8 = 2.  The larger integer is 2.

 

CHECK:

 

    2 - 8 = -6

 

    -5(-6) = 2 + 28

    36 = 26