The number 24 is divided into two parts. Let the first part be $x$ and the second part be $y$. We are given that $7x + 5y = 146$. We also know that $x + y = 24$. The problem asks us to find the value of $x$, the first part.

1. Problem Description

The number 24 is divided into two parts. Let the first part be $x$ and the second part be $y$. We are given that $7x + 5y = 146$. We also know that $x + y = 24$. The problem asks us to find the value of $x$, the first part.

2. Solution Steps

We have two equations:

$x + y = 24$

$7x + 5y = 146$

We can solve this system of equations using substitution or elimination. Let's use substitution. From the first equation, we can express $y$ in terms of $x$:

$y = 24 - x$

Now substitute this expression for $y$ into the second equation:

$7x + 5(24 - x) = 146$

$7x + 120 - 5x = 146$

$2x + 120 = 146$

$2x = 146 - 120$

$2x = 26$

$x = \frac{26}{2}$

$x = 13$

Now, we can find the value of $y$:

$y = 24 - x = 24 - 13 = 11$

We are looking for the first part, which is $x$.

$x = 13$

3. Final Answer

The first part is

1

3. (b) 13