A two-digit number is increased by 5y when the digits are reversed. If the sum of the digits is 12, find the number.
Oops, sorry. The increase is 54 and not 5y. Typo. So the real word problem is
"A two-digit number is increased by 54 when the digits are reversed. If the sum of the digits is 12, find the number."
10x+y -5=10y+x
x+y=12
solve for x,y you have two equations, two unknowns. If you can't do this, repost.
To find the two-digit number, we can start by assigning variables to the digits of the number. Let's say the tens digit is represented by 'x' and the units digit is represented by 'y'.
Since the sum of the digits is 12, we can write the equation: x + y = 12.
We are also given that when the digits are reversed, the number is increased by 5y. This means that the reversed number is 10y + x. So, the equation can be written as: 10y + x = (10x + y) + 5y.
Now we can simplify the equation by combining like terms: 10y + x = 10x + y + 5y.
Simplifying further: 10y + x = 10x + 6y.
Now let's rearrange the equation to isolate one variable: 10y - 6y = 10x - x.
Simplifying: 4y = 9x.
Since the question asks for a two-digit number, x cannot be 0. So we can start by assuming x = 1.
Plugging in x = 1, the equation becomes: 4y = 9.
However, 9 is not divisible by 4, so x cannot be 1. Let's try x = 2.
Plugging in x = 2, the equation becomes: 4y = 18.
Dividing both sides by 4, we get: y = 4.5.
Since y must be an integer, x cannot be 2 either.
Let's continue the pattern and try x = 3.
Plugging in x = 3, the equation becomes: 4y = 27.
Dividing both sides by 4, we get: y = 6.75.
Again, y must be an integer, so x cannot be 3.
We can continue this process and try x = 4, 5, 6, 7, 8, and 9.
For x = 4, we find y = 9.
For x = 5, we find y = 11.25.
For x = 6, we find y = 13.5.
For x = 7, we find y = 15.75.
For x = 8, we find y = 18.
For x = 9, we find y = 20.25.
Out of all these attempts, only when x = 4 is y an integer. Therefore, the number is 49.