Final answer:
The original number the student is looking for is 24, obtained by setting up an algebraic equation based on the given conditions, simplifying it, and solving for the unknown number 'x'.
Step-by-step explanation:
To find the number in question, let's call this unknown number 'x'. First, we add 12 to 'x' and double the sum, which can be expressed as 2(x + 12). According to the problem, this result is equal to one and a half times what we would get if we doubled the original number and then added 12, which is expressed as 1.5(2x + 12).
We can set up the equation as: 2(x + 12) = 1.5(2x + 12). We can simplify this equation by dividing both sides by 0.40 to remove the fractional coefficient, which is equivalent to multiplying both sides by 2.5. This gives us 5(x + 12) = 3(2x + 12), moving 12 into the numerator on the left side and the 0.40 into the denominator on the right side.
Now we can simplify and solve the equation:
5x + 60 = 6x + 36
Bring all x terms to one side: 60 - 36 = 6x - 5x
Simplify: 24 = x
Therefore, the original number the student is looking for is 24.