A number consists of two digits. The sum of 3 times the units digit and 4 times the units digit is 24. If the digits are reversed, the new number is 25 less than the original number. Find the number
To solve this problem, let's represent the tens digit as 'x' and the units digit as 'y'.
According to the problem statement, the number consists of two digits, so it can be represented as 10x + y.
From the given information, we can form the following equation based on the sum of the digits:
3y + 4y = 24
Simplifying the equation:
7y = 24
To solve for 'y', we divide both sides of the equation by 7:
y = 24 / 7
Calculating the value of 'y':
y = 3 and a remainder of 3
Since 'y' represents the units digit, it can only be a single digit. Therefore, 'y' cannot be equal to 3, so this solution is not valid.
Now, let's consider the second piece of information: if the digits are reversed, the new number is 25 less than the original number. This can be represented as:
(10y + x) - 25 = 10x + y
Simplifying the equation:
10y + x - 25 = 10x + y
Rearranging the equation:
9y - 9x = 25
From this equation, we notice that both 'y' and 'x' are equal to 3. Plugging these values back into the original equation:
10y + x = 10x + y
10(3) + 3 = 10(3) + 3
30 + 3 = 30 + 3
33 = 33
The equation is balanced, and the solution is valid. Therefore, the number is 33.