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

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Question 1161044: 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 3 solutions by josgarithmetic, ankor@dixie-net.com, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
10t%2Bu, the number

t%3Cu
and
u-t=1


10t%2Bu=1%2B5%28t%2Bu%29

Substituting for u:
10t%2Bt%2B1=1%2B5%28t%2Bt%2B1%29
11t%2B1=1%2B10t%2B5
11t=10t%2B5
highlight%28t=5%29

The Number highlight%28highlight%2856%29%29

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
a = the 10's digit
b = the units
:
Write an equation for each statement
:
The difference between the digits of a two-digit number is 1.
b - a = 1 (unit is greater than the 10's)
b = a + 1
The number itself is 1 more than 5 times the sum of its digits.
10a + b = 5(a+b) + 1
10a + b = 5a + 5b + 1
10a - 5a = 5b - b + 1
5a = 4b + 1
replace b with (a+1)
5a = 4(a+1) + 1
5a = 4a + 4 + 1
5a - 4a = 4
a = 5
therefore
b = 5 + 1
b = 6
The number is 56

:


Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


A quick and easy path to the solution, using logical reasoning -- if a formal algebraic solution is not required.

"the number itself is 1 more than 5 times the sum of its digits".

1 more than a multiple of 5 means the units digit of the number is either 1 or 6.

The units digit is 1 more than the tens digit; so the 2-digit number is either "01" or "56".

"01" is not a 2-digit number. "56" is; and it satisfies the condition that the number is 1 more than 5 times the sum of its digits.

ANSWER: 56