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.
Algebra ->
Proportions
-> 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.
Log On
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.
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)
