Question

Adelivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 45 pounds each, and the small boxes weigh 30 pounds each. There

are 125 bones in all of the truck is corrying a total of 4800 pounds in boxes, how many of each type of box is it carrying?

Answer 1

TOPIC: 2x2 system of equations

Be,

x = number of large boxes

y = number of small boxes

According to the statement there are 125 boxes (large and small) in a truck, so

x + y = 125 (Equation 1)

We are also told that the large boxes weigh 45 pounds, so

45x --> Weight of an "x" number of large boxes

And the small boxes 30 pounds

30y --> Weight of a "y" number of small boxes

According to the statement, the weight of the 125 boxes (large and small) is 4800 pounds, so

45x + 30y = 4800 (Equation 2)

Our system of equations is:

x + y = 125

45x + 30y = 4800

To solve this system we will apply the equalization method, which consists of solving for the same variable (x or y) in each equation.

In this case we will isolate x.

From the first equation

x = 125 - y

And from the second equation

45x = 4800 - 30y

`\mathsf{x = (4800-30y)/(45) }`

We equate both expressions

`\mathsf{125 - y = (4800-30y)/(45) }\\\\\mathsf{45(125-y)=4800 - 30y}\\\\\mathsf{5625 - 45y = 4800 - 30y}\\\\\mathsf{5625 - 4800 = 45y - 30y}\\\\\mathsf{825 = 15y}\\\\\mathsf{(825)/(15)=y }\\\\\mathsf{55 = y}`

There are 55 small boxes in the truck, we need to find the number of large boxes, for this we will use equation 1.

x + y = 125 (Equation 1)

x = 125 - y = 125 - 55

x = 70

Verification

Substituting both x, y into Equation 2, we have that

45x + 30y = 4800

45(70) + 30(55) = 4800

4800 = 4800

Correct!

The answer to your math homework on 2x2 equations is: The truck has 70 large boxes and 55 small boxes.