A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 25

Question

pounds each, and the small boxes weigh 50
pounds each. There are 105
boxes in all. If the truck is carrying a total of 3,875
pounds in boxes, how many of each type of box is it carrying?
A. 5 10
B.50 55
C.38 75
D.55 50

Answer 1

To solve the problem, we can set up a system of equations based on the information provided.

Let's denote:

• \( x \) as the number of large boxes
• \( y \) as the number of small boxes

We have two equations based on the information given:

1. The total number of boxes: \[ x + y = 105 \]

2. The total weight of the boxes: \[ 25x + 50y = 3875 \]

Now we can solve this system of equations step by step.

First, we can use the first equation to solve for \( y \): \[ y = 105 - x \]

Now we can substitute this expression for \( y \) into the second equation: \[ 25x + 50(105 - x) = 3875 \]

Expanding this gives: \[ 25x + 5250 - 50x = 3875 \]

Combining like terms: \[ -25x + 5250 = 3875 \]

Subtracting 5250 from both sides: \[ -25x = 3875 - 5250 \] \[ -25x = -1375 \]

Dividing by -25: \[ x = 55 \]

Now we can substitute \( x \) back into the equation for \( y \): \[ y = 105 - x = 105 - 55 = 50 \]

Thus, the truck is carrying:

• 55 large boxes
• 50 small boxes

So the answer is: D. 55 large boxes and 50 small boxes.