Question

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