The units digit of a two digit number is 1 more than twice the tens digit. If the digits are reversed, the new number is 36 more than the original number. Find the number.
Please help!!
Sure, I'll help you find the number in my own unique way! Let's call the tens digit "T" and the units digit "U". According to the problem, we have two equations:
1) U = 2T + 1 (The units digit is 1 more than twice the tens digit)
2) 10U + T = 10T + U + 36 (The reversed number is 36 more than the original number)
Let's solve this using my comical approach! *Drumroll, please*
We can start by substituting equation 1 into equation 2. So instead of writing U in equation 2, we'll write (2T + 1). Let's do the math:
10(2T + 1) + T = 10T + (2T + 1) + 36
Now, let's distribute and simplify:
20T + 10 + T = 10T + 2T + 1 + 36
21T + 10 = 12T + 37
Oh no! We ended up with a math problem that is trickier to solve than trying to juggle a dozen eggs. But worry not, for I shall prevail!
Let's move all the terms with T to one side and all the constants to the other side:
21T - 12T = 37 - 10
9T = 27
Now, let's divide both sides by 9:
T = 27/9
T = 3
Ta-da! The tens digit is 3.
Now that we know the tens digit, we can substitute it back into equation 1 to find the units digit:
U = 2T + 1
U = 2(3) + 1
U = 6 + 1
U = 7
And there you have it! The units digit is 7.
Putting the tens and units digit together, we get the number: 37.
So, the number we're looking for is 37. Voila!
Let's start by assuming the tens digit is 'x' and the units digit is 'y'.
From the given information, we know that the units digit 'y' is 1 more than twice the tens digit 'x'. So, we can write the first equation as:
y = 2x + 1 ..............(Equation 1)
We also know that when the digits are reversed, the new number is 36 more than the original number. This can be expressed as:
10y + x = 10x + y + 36
Simplifying this equation further, we get:
10y - y = 10x - x + 36
9y = 9x + 36
Dividing both sides by 9:
y = x + 4 ...............(Equation 2)
Now, we can solve these two equations simultaneously to find the values of x and y.
Substituting the value of y from Equation 2 into Equation 1:
x + 4 = 2x + 1
Subtracting x from both sides:
4 = x + 1
Subtracting 1 from both sides:
3 = x
Substituting the value of x into Equation 2:
y = 3 + 4
y = 7
So, the tens digit 'x' is 3, and the units digit 'y' is 7.
Therefore, the number is 37.
To solve this problem, we will first represent the two-digit number using variables and then set up equations based on the given information.
Let's assume the tens digit is "x" and the unit digit is "y". Therefore, the original number can be represented as 10x + y.
According to the problem statement, the units digit (y) is 1 more than twice the tens digit (2x). We can write this as:
y = 2x + 1
Furthermore, if the digits are reversed, the new number is 36 more than the original number. This can be written as:
10y + x = 10x + y + 36
Now we have a system of two equations with two variables:
Equation 1: y = 2x + 1
Equation 2: 10y + x = 10x + y + 36
To solve this system of equations, we can substitute the value of y from Equation 1 into Equation 2:
10(2x + 1) + x = 10x + (2x + 1) + 36
Simplify and solve for x:
20x + 10 + x = 10x + 2x + 1 + 36
21x + 10 = 12x + 37
9x = 27
x = 3
Now that we have the value of x, we can substitute it back into Equation 1 to find the value of y:
y = 2x + 1
y = 2(3) + 1
y = 6 + 1
y = 7
Therefore, the two-digit number is 10x + y = 10(3) + 7 = 30 + 7 = 37.
So the number is 37.
let the unit digit be x
let the tens digit by y
x = 2y+1
so the original number is 10y + x
and the number reversed would by 10x + y
so 10x+y - (10y+x) = 36
9x - 9y = 36
x - y = 4
(2y+1) - y = 4
y = 3 , then x = 7
the original number was 37