Question

a delivery truck is transporting boxes of two sizes: large and small. the combined weight of a large box and a small box is 65 pounds. the truck is transporting 50 large boxes and 70 small boxes. if the truck is carrying a total of 3650 pounds in boxes, how much does each type of box weigh?
large box: (square) pounds
small box: (square) pounds

Explanation:

Step1: Define variables

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

Step2: Set up equations

1. Combined weight: $L + S = 65$
2. Total weight: $50L + 70S = 3650$

Step3: Simplify total weight equation

Divide second equation by 10: $5L + 7S = 365$

Step4: Isolate $L$ from first equation

$L = 65 - S$

Step5: Substitute $L$ into simplified equation

$5(65 - S) + 7S = 365$
$325 - 5S + 7S = 365$
$325 + 2S = 365$

Step6: Solve for $S$

$2S = 365 - 325 = 40$
$S = \frac{40}{2} = 20$

Step7: Solve for $L$

$L = 65 - 20 = 45$

Answer:

Large box: 45 pounds
Small box: 20 pounds