SOLUTION: The difference between the digits of a two-digit number is 1. The number itself is 1 more than 5 times the sum of its digits. If the units digit is greater than the tens digit, fin

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The difference between the digits of a two-digit number is 1. The number itself is 1 more than 5 times the sum of its digits. If the units digit is greater than the tens digit, fin      Log On


   

Question 1140726: The difference between the digits of a two-digit number is 1. The number itself is 1 more than 5 times the sum of its digits. If the units digit is greater than the tens digit, find the number
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
t, Tens digit
u, Ones digit
u%3Et

system%28u-t=1%2C10t%2Bu=5%28u%2Bt%29%29
Solving this system should not be complicated.


45

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(1) Using logical reasoning....

The number is 1 more than 5 times the sum of its digits.
That means the last digit of the number (the units digit) is either 1 or 6.
Since the units digit is 1 more than the tens digit, the units digit can't be 1.
So the units digit is 6; that means the tens digit is 5.

ANSWER: 56

(2) Using algebra (good practice in solving problems using algebra; but much slower)....

Let the tens digit be x
Then the units digit is x+1

The sum of the digits is x+(x+1) = 2x+1

The number itself is 10(x)+(x+1) = 11x+1

The number itself is 1 more than 5 times the sum of the digits:

11x%2B1+=+5%282x%2B1%29%2B1
11x%2B1+=+10x%2B6
x+=+5

ANSWER: The tens digit is x=5; the units digit is x+1 = 6; the number is 56.