A fruit company dellvers Its fruit in two types of boxes: large and small. A delivery of 3 large boxes and 5 small boxes has a total welght of 116 kllograms. A dellvery of 9 large boxes and 7 small boxes has a total weight of 238 kllograms. How much does each type of box welgh?

Let the weight of a large box be \( L \) kilograms and the weight of a small box be \( S \) kilograms.

We have the following two equations based on the problem statement:

1. \( 3L + 5S = 116 \) (for the delivery of 3 large boxes and 5 small boxes)
2. \( 9L + 7S = 238 \) (for the delivery of 9 large boxes and 7 small boxes)

Now, we can solve these equations simultaneously.

First, multiply the first equation by 3 to align the coefficients of \( L \):

\[
3(3L + 5S) = 3(116)
\]

This gives us:

\[
9L + 15S = 348 \quad \text{(Equation 3)}
\]

Now we have:

- \( 9L + 15S = 348 \) (Equation 3)
- \( 9L + 7S = 238 \) (Equation 2)

Next, subtract Equation 2 from Equation 3 to eliminate \( L \):

\[
(9L + 15S) - (9L + 7S) = 348 - 238
\]

This simplifies to:

\[
8S = 110
\]

Now, divide both sides by 8:

\[
S = \frac{110}{8} = 13.75
\]

So, the weight of a small box is \( 13.75 \) kilograms. Now, substitute \( S \) back into one of the original equations to find \( L \). We'll use Equation 1:

\[
3L + 5S = 116
\]

Substituting \( S = 13.75 \):

\[
3L + 5(13.75) = 116
\]
\[
3L + 68.75 = 116
\]

Subtract \( 68.75 \) from both sides:

\[
3L = 116 - 68.75
\]
\[
3L = 47.25
\]

Now, divide by 3:

\[
L = \frac{47.25}{3} = 15.75
\]

Thus, the weights of the boxes are:
- Large box: \( 15.75 \) kilograms
- Small box: \( 13.75 \) kilograms