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