The units digit of a two-digit number is 1 less than its tens digit. The sum of the number when digits are reversed and the original number is 77. Find the original number.
Answers
Let T represent the ten’s digit and U represent the unit’s digit.
The unit’s digit is 11 less than twice the ten’s digit:
U = 2T - 11
The number is 6 less than 7 times the sum of the digits.
10T + U = 7(T + U) - 6
Substitute 2T - 11 for U (using the first equation) into the second equation:
10T + (2T - 11) = 7(T + (2T - 11)) - 6
12T - 11 = 7(3T - 11) - 6
12T - 11 = 21T - 77 - 6
12T - 11 = 21T - 83
12T + 72 = 21T (adding 83 to both sides and simplifying)
72 = 9T (subtracting 12T from both sides and simplifying)
8 = T
U = 2T - 11
= 2(8) - 11
= 16 - 11
= 5
The ten’s digit is 8 and the unit’s digit is 5; the original number is 85.
See if you can do the rest of your assignment by yourself.
I know this is the word to word answers but relate to this and solve your questions