The product of two consecutive integers is 56. How do you find the integers?

1 Answer
Tony B
Jun 2, 2016

The two numbers are 7 and 8.

Explanation:

#color(blue)("From the multiplications tables")#

#color(green)(7xx8=56)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("The algebra way")#
Let the first number be #n#

Then the second number is #n+1#

The product is #nxx(n+1) = 56#

#=>n^2+n-56=0#

Known: #7xx8=56#. However the equation's 56 is nagetive, so one of the 7 and 8 is negative.
The equation has #+n# so the larger of the two is positive. Giving:

#(n-7)(n+8)=0#

#=> n = +7" and "n=-8#

As a first number #n=-8# is not logical so the first number is #n=7#

Thus the second number is 8.

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