Understanding the Problem
To solve the problem, we need to define two numbers. Let's denote them as 'x' and 'y'. We know the following from the problem statement:
- The greater of the two numbers is 12 smaller than the sum of the numbers.
- The sum of the two numbers is 10.
Setting Up the Equations
From the information, we can form two equations:
1. The sum of the two numbers:
- x + y = 10
2. The greater number (let's assume x is greater) is 12 smaller than the sum:
- x = (x + y) - 12
Substituting and Simplifying
We can substitute the first equation into the second equation:
- x = (10) - 12
- x = -2
Now, substituting x back into the first equation:
- -2 + y = 10
- y = 10 + 2
- y = 12
Conclusion
The values we found are:
- x = -2
- y = 12
However, since we assumed x was the greater number, we need to ensure our solution aligns with the conditions stated in the problem.
Final Verification
1. Check the sum:
- -2 + 12 = 10 (correct)
2. Check if the greater number is indeed 12 smaller than the sum:
- The greater number (12) is 12 smaller than the sum (10), which does not hold true.
Thus, reevaluating our assumptions and calculations is crucial. We must ensure that the numbers make logical sense based on the problem conditions.
Hence, the solution needs a careful approach in identifying which number is greater and validating the conditions provided in the problem statement.