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Answer: 47
Step-by-step explanation: To solve this problem, let's use <em>t</em> to represent our tens digit and <em>u</em> to represent our units digit so that the value of our number can be represented as 10<em>t</em> + <em>u</em>.
If we represent the value of our number as 10<em>t</em> + <em>u</em>, the value of the number with the digits reversed can be represented as 10<em>u</em> + <em>t</em>.
Since the first sentence states that the sum of the digits of a two-digit number is 11, that's <em>t </em>+<em> u</em> = 11.
Reading through our second sentence, when the digits are reversed, the new number is 27 more than the original number, that's 10<em>u</em> + <em>t</em> "is" which means equals 27 more than the original number that's 10<em>t </em>+ <em>u</em> + 27.
So 10<em>t</em> + <em>u</em> = 10<em>t</em> + <em>u</em> + 27.
Before solving this system however, let's rearrange our second equation so that the t's and u's are on the same side by subtracting 10<em>t</em> and <em>u</em> from both sides to get 9<em>u</em> - 9<em>t</em> = 27 and when we rewrite our first equation above it, instead of writing it as <em>t</em> + <em>u</em> = 11, let's write it as <em>t</em> + <em>u</em> = 11 so that our u's and t's will match up in the system.
To solve this system, let's use addition so multiply the top equation by 9 to get 9<em>u </em>+ 9<em>t</em> = 99 and 9<em>u</em> - 9<em>t</em> = 27 so that when we add the equations together the t's cancel and we get 18<em>u</em> = 126. Dividing both sided by 18, <em>u </em>= 7.
To find <em>t</em>, plug 7 back in for <em>u</em> in our first equation to get <em>t</em> + 7 = 11. Subtract 7 from both sides and <em>t</em> = 4.
Since our tens digit is 4 and our units is 7, our number must be 47.
I have also attached my work on a whiteboard.
