SOLUTION: a number between 10 and 100 is five times the sum of its digits. if 9 be added to it the digits are reversed, find the number.....??????

Question 444191: a number between 10 and 100 is five times the sum of its digits. if 9 be added to it the digits are reversed, find the number.....??????
Answer by chriswen(106) (Show Source): You can put this solution on YOUR website!
Let x be the first digit.
Let y be the second digit.
...
5(x+y)=10x+y ...(i)
5x+5y=10x+y
5y-y=10x-5x
4y=5x ...(ii)
...
The 10x+y is because the x digit is in the ten's column and it is worth more.
...
10x+y+9=10y+x ...(iii)
10x-x+9=10y-y
9x+9=9y
9(x+1)=9y
x+1=y ...(iv)
substitute x+1=y into (ii)
4(x+1)=5x ...(v)
4x+4=5x
4=5x-4x
x=4
substitute x=4 into (ii)
4y=5(4)
4y=20
y=20/4
y=5
...
The first digit is 4. The second digit is 5.
The number is 45.
RELATED QUESTIONS
A certain number is between 10 and 100. Its value is 8 times the sum of its digits and if (answered by greenestamps)

A two digit number is 4 times the sum of its digits. If 27 is added to that number its... (answered by josmiceli)

a number consists of two digits whose sum is 9.if 9 is added to the number ,its... (answered by checkley79)

The sum of two digits of a two digit number is 15. If 9 is added to it, the digits are... (answered by richwmiller,Boreal,htmentor)

The difference between the two digits of a number less than 100 is 2. If 3/2 times the... (answered by josmiceli,KMST)

number of two digit exceeds 4 times the sum of the digits by 3 if 36 is added to the... (answered by ptfile)

6) If twenty seven is added to a two digit #, the original # will be reversed. The number (answered by solver91311)

a number lies between 10 & 100. the number is 8 times the sum of its digits & when 45 is... (answered by josgarithmetic)

The sum of the digits of a two-digit number is 11. If 27 is added to the number, the... (answered by checkley75)