Questions: A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 3 large boxes and 2 small boxes has a total weight of 83 kilograms. A delivery of 5 large boxes and 6 small boxes has a total weight of 175 kilograms. How much does each type of box weigh? Weight of each large box: kilogram(s) Weight of each small box: kilogram(s)

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 3 large boxes and 2 small boxes has a total weight of 83 kilograms. A delivery of 5 large boxes and 6 small boxes has a total weight of 175 kilograms. How much does each type of box weigh?

Weight of each large box: kilogram(s)
Weight of each small box: kilogram(s)

Transcript text: A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 3 large boxes and 2 small boxes has a total weight of 83 kilograms. A delivery of 5 large boxes and 6 small boxes has a total weight of 175 kilograms. How much does each type of box weigh? Weight of each large box: $\square$ kilogram(s) Weight of each small box: kilogram(s)

Solution

Solution Steps

Step 1: Formulate the equations

The system of equations based on the given scenarios is:

$3L + 2S = 83$
$5L + 6S = 175$

Step 2: Apply Cramer's Rule

To solve the system, we use Cramer's Rule, which requires calculating the determinant of the system's matrix. The determinant is calculated as $det = a_d - b_c = 3_6 - 2_5 = 8$. Since the determinant is not zero, the system has a unique solution.

Step 3: Solve for L and S using Cramer's Rule

Using Cramer's Rule, we find: $L = \frac{W1_d - b_W2}{det} = \frac{83_6 - 2_175}{8} = 18.5$ $S = \frac{a_W2 - W1_c}{det} = \frac{3_175 - 83_5}{8} = 13.75$