SOLUTION: The units� digit of a two-digit number is 7 more than the tens� digit. If 26 is added to the number, the result obtained is five times the sum of the digits. Find the number.

Question 1066653: The units� digit of a two-digit number is 7 more than the tens� digit. If 26 is added to the number, the result obtained is five times the sum of the digits. Find the number.

Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
Let a = unit's digit
Let b = ten's digit
�
In this way, 10b+a = the unknown number
�
a = b+7 (1)
(10b+a) + 26 = 5(a+b) (2)
Subs "b+7" for "a" from (1), into (2):
(10b + (b+7)) + 26 = 5((b+7) + b)
(10b + b + 7 + 26) = 5(2b+7)
11b + 33 = 10b + 35
11b + 33 - 10b - 33 = 10b + 35 - 10b - 33 (subtract 33 & 10b from both sides)
b = 2
b=2 �(from (1))�> a = 2+7 = 9
�
Ans: the number is 29
�
Check: 2+9 = 11, and 11*5 = 55
and 29 + 26 = 55 (ok)

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