Question

A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 50 pounds each, and the small boxes weigh 25 pounds each. There are 135 boxes in all. If the truck is carrying a total of 5125 pounds in boxes, how many of each type of box is it carrying?

Answer 1

Let’s call the number of large boxes “L” and the number of small boxes “S”. We know that there are 135 boxes in total, so we can write:

L + S = 135

We also know that the total weight of all the boxes is 5125 pounds. Since each large box weighs 50 pounds and each small box weighs 25 pounds, we can write:

50L + 25S = 5125

Now we have two equations with two variables. We can solve for one variable in terms of the other in one equation and substitute that expression into the other equation to solve for the remaining variable.

Let’s solve for L in terms of S in the first equation:

L = 135 - S

Now we can substitute this expression for L into the second equation:

50(135 - S) + 25S = 5125

Distributing the 50:

6750 - 50S + 25S = 5125

Combining like terms:

6750 - 25S = 5125

Subtracting 6750 from both sides:

-25S = -1625

Dividing both sides by -25:

S = 65

So there are 65 small boxes. We can use either equation to solve for L:

L + S = 135

L + 65 = 135

L = 70

So there are 70 large boxes.

Therefore, there are 70 large boxes and 65 small boxes on the truck.

Explanation: