The sum of consecutive integers is 203. What are the two numbers?

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Answer 1 · 2017-07-27T19:46:11

#101# and #102#

#101 + 102=203#

Answer 2 · 2017-07-27T19:47:40

See a solution process below:

First, let's name the first integer: #n#

Then, the second consecutive integer would be #n + 1#

We then can write from the information in the problem:

#n + (n + 1) = 203#

Solving for #n# gives:

#n + n + 1 = 203#

#1n + 1n + 1 = 203#

#(1 + 1)n + 1 = 203#

#2n + 1 = 203#

#2n + 1 - color(red)(1) = 203 - color(red)(1)#

#2n + 0 = 202#

#2n = 202#

#(2n)/color(red)(2) = 202/color(red)(2)#

#(color(red)(cancel(color(black)(2)))n)/cancel(color(red)(2)) = 101#

#n = 101#

Therefore,

The first integer is: #n = 101#

The second integer is: #n + 1 = 101 + 1 = 102#

#101 + 102 = 203#