Let's solve the given problem step by step.
1. Define the variables:
Let \(\( x \)\) be the first number and \(\( y \)\) be the second number.
2. Set up the equations based on the given information:
- The sum of the two numbers is 42:
\(\[ x + y = 42 \]\)
- Twice the first is equal to 3 times the second:
\(\[ 2x = 3y \]\)
3. Solve the system of equations:
From the second equation, solve for \(\( y \)\):
\(\[ 2x = 3y \]\)
\(\[ y = \frac{2x}{3} \]\)
Now substitute \(\( y = \frac{2x}{3} \)\) into the first equation:
\(\[ x + \frac{2x}{3} = 42 \]\)
To clear the fraction, multiply everything by 3:
\(\[ 3x + 2x = 126 \]\)
Combine like terms:
\(\[ 5x = 126 \]\)
Solve for \(\( x \)\):
\(\[ x = \frac{126}{5} \]\)
\(\[ x = 25.2 \]\)
4. Find \(\( y \)\) using \(\( y = \frac{2x}{3} \)\):
\(\[ y = \frac{2(25.2)}{3} \]\)
\(\[ y = \frac{50.4}{3} \]\)
\(\[ y = 16.8 \]\)
5. Determine the larger number:
The two numbers are \(\( x = 25.2 \)\) and \(\( y = 16.8 \)\).
The largest of the two numbers is:
\(\[ \boxed{25.2} \]\)
So, the correct answer is:
C) 25.2
