What is the larger of 2 consecutive integers if their sum is 171?

1 Answer
May 22, 2018

See a solution process below:

Explanation:

First, let's cal the first integer we are looking for: #n#

Then, because we are looking for consecutive integers the second integer we are looking for can be written as: #n + 1#

We know these two integers sum to 171. Therefore, we can write this equation and solve for #n#:

#n + (n + 1) = 171#

#n + n + 1 = 171#

#1n + 1n + 1 = 171#

#(1 + 1)n + 1 = 171#

#2n + 1 = 171#

#2n + 1 - color(red)(1) = 171 - color(red)(1)#

#2n + 0 = 170#

#2n = 170#

#(2n)/color(red)(2) = 170/color(red)(2)#

#(color(red)(cancel(color(black)(2)))n)/cancel(color(red)(2)) = 85#

#n = 85#

  • The First integer is: #85#

  • The Second integer, the larger integer, is: #85 + 1 = 86#

Solution Check:

#85 + 86 = 171#