The sum of two consecutive positive integers is 85. How do you find the integers?

Jul 29, 2016

42 and 43

Explanation:

Start by letting one of the integers be n

Then the next integer (+1) will be n+1

The sum of the integers is then

n + n + 1 = 2n + 1 and since the sum of both = 85 , then.

$\Rightarrow 2 n + 1 = 85$

subtract 1 from both sides of the equation

$\Rightarrow 2 n + \cancel{1} - \cancel{1} = 85 - 1 \Rightarrow 2 n = 84$

divide by 2 to solve for n.

$\Rightarrow \frac{{\cancel{2}}^{1} n}{\cancel{2}} ^ 1 = \frac{{\cancel{84}}^{42}}{\cancel{2}} ^ 1$

so n = 42 and n+ 1 = 42 + 1 = 43

Thus the consecutive integers are 42 and 43