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?

Answer 1

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