Final answer:
When solving the system of equations representing the two numbers that sum up to 52, where the larger number is 4 more than twice the smaller one, the calculated smaller number is 16 and the larger number is 36. However, these numbers do not match any of the provided options, suggesting an error in the options given or in the calculation.
Step-by-step explanation:
The problem given states that the sum of two numbers is 52, and the larger number is 4 more than twice the smaller number. By letting x be the smaller number, we can set up the following equations to solve for the two numbers:
- x + y = 52 (Equation 1: Sum of numbers)
- y = 2x + 4 (Equation 2: Larger number in terms of the smaller one)
Now, we substitute Equation 2 into Equation 1:
- x + (2x + 4) = 52
- 3x + 4 = 52
- 3x = 52 - 4
- 3x = 48
- x = 48 / 3
- x = 16
Now that we know the smaller number (x), we can find the larger number (y) using Equation 2:
- y = 2(16) + 4
- y = 32 + 4
- y = 36
However, upon reviewing the options we realize no option has '36' as the larger number, which means there was likely an error in the transcription of options or the calculation should be verified. As such, the consistent method above does not yield an answer matching the given options, and should be checked for accuracy.