One integer is 3 more than another. Their product is 70. How do you find the integers?

1 Answer
Apr 4, 2018

Answer:

#(7,10)# or #(-7,-10)#

Explanation:

Let the integers be #x# and #y# (where let’s say #x > y#)

Conditions given are

  • #x = y + 3#

  • #xy = 70#

First equation can be written as

#x = 70/x + 3#

#x - 70/x = 3#

#(x^2 - 70)/x = 3#

#x^2 - 70 = 3x#

#x^2 - 3x - 70 = 0#

#x^2 + 10x - 7x - 70 = 0#

#x(x + 10) - 7(x + 10) = 0#

#(x -7)(x + 10) = 0#

#x = -7# or #x = 10#

If #x = -7#

Value of #y# from first equation is

#y = x - 3 = -7 - 3 = -10#

If #x = 10#

Value of #y# from first equation is

#y = x - 3 = 10 - 3 = 7#

Therefore, two sets of integers are possible: #(-7,-10)# and #(7, 10)#