A two digit number is 4 times the sum of its digits .The sum of the number formed by reversing its digits and 9is equal to 2 times the original number find the number
10a+b = 4(a+b)
10b+a + 9 = 2(10a+b)
The number is 36
check:
36 = 4(3+6)
63+9 = 2(36)
yep.
To find the two-digit number, we need to set up equations based on the given information. Let's call the tens digit of the number "x" and the ones digit "y".
1) "A two-digit number is 4 times the sum of its digits."
This can be written as an equation: 10x + y = 4(x + y)
2) "The sum of the number formed by reversing its digits and 9 is equal to 2 times the original number."
The number formed by reversing the digits is 10y + x. So the equation becomes: (10y + x) + 9 = 2(10x + y)
Now, let's solve the equations step by step:
1) Expand the equations:
10x + y = 4x + 4y
10y + x + 9 = 20x + 2y
2) Simplify the equations:
10x - 4x + y - 4y = 0
20x - x - 2y - 10y - 9 = 0
3) Combine like terms:
6x - 3y = 0
19x - 12y - 9 = 0
4) Solve the first equation for x:
6x = 3y
x = (3y)/6
x = y/2
5) Substitute x in the second equation:
19(y/2) - 12y - 9 = 0
19y/2 - 12y - 9 = 0
6) Multiply through by 2 to get rid of the fractions:
19y - 24y - 18 = 0
-5y - 18 = 0
7) Add 18 to both sides:
-5y = 18
y = -18/5
y = -3.6
However, we are looking for a two-digit number, so the tenths place cannot be a decimal. Therefore, there is no solution to this problem.