delivery truck is transporting a box of two sizes large and small the large boxes weigh 50 pounds each and a small box is weigh 15 pound each There are 120 boxes in all If the truck is carrying a total of 3725 pounds in boxes how many boxes of each type of box is it carrying?

a of large and b of small

50 a + 15 b = 3725
a + b = 120
multiply second equation by 15 for example
50 a + 15 b = 3725
15 a + 15 b = 1800
--------------------------- subtract
35 a + 0 = 1925
a = 55
go back and get b

Let's assume the number of large boxes is represented by "L" and the number of small boxes is represented by "S."

We are given two pieces of information:

1. The large boxes weigh 50 pounds each.
2. The small boxes weigh 15 pounds each.

Based on the information given, we can set up two equations:

1. L + S = 120 (The total number of boxes is 120)
2. 50L + 15S = 3725 (The total weight is 3725 pounds)

We can solve this system of equations to find the values of L and S.

We'll use the substitution method to solve this system.

From equation 1, we have L = 120 - S.

Substituting this value of L into equation 2, we get:

50(120 - S) + 15S = 3725

Simplifying this equation:

6000 - 50S + 15S = 3725

Combine like terms:

-35S = -2275

Divide both sides by -35:

S = 65

Now that we have the value of S, we can substitute it back into equation 1 to find L:

L = 120 - S = 120 - 65 = 55

Therefore, the truck is carrying 55 large boxes and 65 small boxes.

To solve this problem, we can use a system of equations. Let's denote the number of large boxes as "L" and the number of small boxes as "S".

From the given information, we know that:
1. Each large box weighs 50 pounds.
2. Each small box weighs 15 pounds.
3. The total number of boxes is 120.
4. The total weight of the boxes is 3725 pounds.

Using these facts, we can set up the following equations:

Equation 1: L + S = 120 (total number of boxes)
Equation 2: 50L + 15S = 3725 (total weight of the boxes)

We can now solve this system of equations.

To solve Equation 1, we can isolate L:
L = 120 - S

Substituting this into Equation 2:
50(120 - S) + 15S = 3725

We can simplify the equation:
6000 - 50S + 15S = 3725
-35S = 3725 - 6000
-35S = -2275

Dividing both sides by -35:
S = -2275 / -35
S = 65

Now, substitute the value of S back into Equation 1 to find L:
L = 120 - S
L = 120 - 65
L = 55

Therefore, the truck is carrying 55 large boxes and 65 small boxes.