Question 1153592
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Four times the ones digit of a positive, two digit integer is 25 greater than the sum of the digits. Reversing the digits increases the number by 63. What is the number?
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u, the ones digit
t, the tens digit

u+10t, the two-digit number


The description:
{{{system(4u=25+u+t,10u+t=63+(u+10t))}}}
Simplify.



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{{{system(3u-t=25,9u-9t=63)}}}
-
{{{system(3u-t=25,u-t=7)}}}


Finish to solve.  {{{E1-E2}}}
{{{(3u-t)-(u-t)=25-7}}}
{{{3u-t-u+t=18}}}
{{{2u=18}}}
{{{highlight(u=9)}}}


{{{u-t=7}}}
{{{-t=7-u}}}
{{{t=u-7}}}
{{{highlight(t=2)}}}


The number is  29.