Question

a fruit company delivers its fruit in two types of boxes: large and small. a delivery of 5 large boxes and 2 small boxes has a total weight of 117 kilograms. a delivery of 3 large boxes and 8 small boxes has a total weight of 162 kilograms. how much does each type of box weigh?
weight of each large box: □ kilogram(s)
weight of each small box: □ kilogram(s)

Explanation:

Step1: Define variables

Let $L$ = weight of large box, $S$ = weight of small box.

Step2: Set up equations

$$5L + 2S = 117$$
$$3L + 8S = 162$$

Step3: Eliminate one variable

Multiply first equation by 4: $20L + 8S = 468$
Subtract second equation: $(20L + 8S) - (3L + 8S) = 468 - 162$
Simplify: $17L = 306$

Step4: Solve for $L$

$$L = \frac{306}{17} = 18$$

Step5: Solve for $S$

Substitute $L=18$ into $5L + 2S = 117$:
$5(18) + 2S = 117$
$90 + 2S = 117$
$2S = 117 - 90 = 27$
$$S = \frac{27}{2} = 13.5$$

Answer:

Weight of each large box: 18 kilogram(s)
Weight of each small box: 13.5 kilogram(s)