SOLUTION: Will you please help me with this word problem. The units digit of a two-digits number is 1 more than 4 times the tens digit. If the digits are reversed, the new number is 5 more

Question 43500: Will you please help me with this word problem. The units digit of a two-digits number is 1 more than 4 times the tens digit. If the digits are reversed, the new number is 5 more than 3 times the original number. Find the original number.
Answer by psbhowmick(878) (Show Source): You can put this solution on YOUR website!
Let the digit in the 10's place be 'x' and that in the unit's place be 'y'.
Then, the number is: 10x + y.
Now, 4 times the digit in 10's = 4x.
According to the problem, digit in unit's place = 4 times digit in ten's place + 1.
So, y = 4x + 1_________(1)

Again, if the digits are reversed then the number becomes: 10y + x.
[As then the digit in 10's place becomes that in unit's place and that in unit's place becomes digit in 10's place]

According to the problem, new number = 3 times original number + 5.
Hence, 10y + x = 3(10x + y) + 5 or 7y - 29x = 5 _________(2)

Substituting the value of 'y' from (1) in (2),
7(4x + 1) - 29x = 5
or 28x + 7 - 29x = 5
or -x = 5 - 7 = -2
or x = 2

Putting x = 2 in (1), we have y = 4(2) + 1 = 9.

Thus, the original number is (10x + y) = = 29.
RELATED QUESTIONS
Good evening ma'am or sir. Would you please help me in solving this word problem: 1).... (answered by stanbon)

please help me with this problem..thank you! the sum of the digits of a three digit... (answered by scott8148)

pls. help me solve this problem... thank you... problem 1. Three times the tens digit (answered by mananth)

Can you please help me solve the following word problem and the formula used to solve it? (answered by Mathtut)

pls. help me solve this problem... thank you... 1. Three times the tens digit of a... (answered by ewatrrr)

A certain two digit number has a value that is three times the sum of it's digits. The... (answered by ankor@dixie-net.com)

please help me solve the problem. Thank you! the units digits of a two-digit number is (answered by ankor@dixie-net.com)

Please help me with this problem: Find the two-digit number whose tens digit is 3 less... (answered by atif.muhammad,kev82)

hello would you please help me with this problem? the tens digit of a two-digit number is (answered by scott8148)