Question 693762
the sum of the digits is 7. when the digits are interchanged, and the resulting number is subtracted from the original one, the difference is 45. what are the digits?


Let the tens and units digits be T and U, respectively


Then: T + U = 7 ----- eq (i)


Original number = 10T + U, and interchanged number = 10U + T


Therefore, 10T + U - (10U + T) = 45 ---- 10T + U - 10U - T = 45 --- 9T - 9U = 45 ---- 9(T - U) = 9(5) ---- T - U = 5 ----  eq (ii)



T + U = 7 -----  eq (i)
T - U = 5 -----  eq (ii)
2T = 12 ----- Adding eqs (ii) & (i)
T, or tens digit = {{{12/2}}}, or {{{highlight_green(6)}}}


6 + U = 7 ------ Substituting 6 for T in eq (i)
U, or units digit = 7 - 6, or {{{highlight_green(1)}}}


You can do the check!!


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