Question

A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weighs 45 pounds and each large box of paper weighs 75 pounds. A total of 22 boxes of paper were shipped weighing 1350 pounds altogether. Determine the number of small boxes shipped and the number of large boxes shipped.

Answer 1

Answer:

Number of small boxes shipped = 10

Number of large boxes shipped = 12

Step-by-step explanation:

Let x be the number of small boxes

and

y be the number of large boxes

According to the first statement, a total of 22 boxes were shipped

Equation 1 will be:

x+y=22

And

According to 2nd statement, Total weight was 1350 and we know the weight of one small box is 45 and large box is 75

So equation 2 will be:

45x+75y=1350

We will use the substitution method for solving the equation

So from equation 1

$x+y=22\\x=22-y$

Putting the value of x in eqn 2

$45x+75y=1350\\45(22-y)+75y=1350\\990-45y+75y=1350\\-45y+75y=1350-990\\30y=360\\\frac{30y}{30}=\frac{360}{30}\\y=12$

Putting the value of y in eqn 1

$x+y=22\\x+12=22\\x=22-12\\x=10$

So,

Number of small boxes shipped = 10

Number of large boxes shipped = 12 ..