SOLUTION: The sum of the digits of a two digit number is 1. The number formed by reversing the number is 4 less than 5 times the number. Find the original number?
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Question 691410: The sum of the digits of a two digit number is 1. The number formed by reversing the number is 4 less than 5 times the number. Find the original number?
Can you please help me out with this question I really don't understand? thanks in advance. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! let a = the 10's digit
let b = the ones
then
10a+b = the two digit number
and
10b+a = the number with reversed digits
:
Write an equation for each statement:
:
"The sum of the digits of a two digit number is 1," indicates that something is wrong as written, no two positive integers are equal to 1
:
Try to solve it without knowing the sum of the digits
:
The number formed by reversing the number is 4 less than 5 times the number.
10b + a = 5(10a+b) - 4
10b + a = 50a + 5b - 4
10b - 5b = 50a - a - 4
5b = 49a - 4
Divide both sides by 9
b = a -
A little thought here reveals that if a = 1, we have
b = -
b =
b = 9
:
a = 1, is the only value that makes b an integer
:
Our number is 19
:
Check this in the statement:
"The number formed by reversing the number is 4 less than 5 times the number."
91 = 5(19) - 4
91 = 95 - 4
:
The 1st statement should have read
The sum of the digits is 10
