Question 1163926
Find a two digit number such that three times the tens digit is 2 less than
twice the units digits and twice the number is 20 greater than the number
obtained by reversing the digits
<pre>Let tens and units digits, be T and U, respectively
Then we get: {{{system(matrix(1,3, 3T, "=", 2U  -  2), matrix(1,6, 3T  -  2U, "=", - 2, "------", eq, "(i)"))}}}           {{{system(matrix(3,3, 2(10T + U), "=", 10U + T + 20, 20T + 2U, "=", 10U + T + 20, 20T  -  T + 2U  -  10U, "=", 20), matrix(1,6, 19T  -  8U, "=", 20, "-------", eq, "(ii)"))}}}
                                                            12T - 8U = - 8 ------- Multiplying eq (i) by 4 ------ eq (iii) 
                                                             7T = 28 ------ Subtracting eq (iii) from eq (ii)
                                                             Tens digit, or {{{matrix(1,5, T, "=", 28/7, "=", 4)}}}

3(4)  -  2U = - 2 ------- Substituting 4 for T in eq (i)
12  -  2U = - 2
-  2U = - 14
Units digit, or {{{matrix(1,5, U, "=", (- 14)/(- 2), "=", 7)}}}

{{{highlight_green(matrix(1,2, "Number:", 47))}}}</pre>