Question

a fruit company delivers its fruit in two types of boxes: large and small. a delivery of 2 large boxes and 5 small boxes has a total weight of 57 kilograms. a delivery of 8 large boxes and 3 small boxes has a total weight of 126 kilograms. how much does each type of box weigh?
weight of each large box: \\(\square\\) kilogram(s)
weight of each small box: \\(\square\\) kilogram(s)

Explanation:

Step1: Define Variables

Let \( l \) be the weight of a large box (in kilograms) and \( s \) be the weight of a small box (in kilograms).

Step2: Set Up Equations

From the problem, we have two equations:

1. \( 2l + 5s = 57 \) (from 2 large and 5 small boxes)
2. \( 8l + 3s = 126 \) (from 8 large and 3 small boxes)

Step3: Solve the System of Equations

First, multiply the first equation by 4 to make the coefficients of \( l \) the same:
\( 8l + 20s = 228 \)
Now subtract the second equation (\( 8l + 3s = 126 \)) from this new equation:
\( (8l + 20s) - (8l + 3s) = 228 - 126 \)
\( 17s = 102 \)
\( s = \frac{102}{17} = 6 \)
Now substitute \( s = 6 \) back into the first equation:
\( 2l + 5(6) = 57 \)
\( 2l + 30 = 57 \)
\( 2l = 57 - 30 = 27 \)
\( l = \frac{27}{2} = 13.5 \)

Answer:

Weight of each large box: \( 13.5 \) kilogram(s)
Weight of each small box: \( 6 \) kilogram(s)