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 24 boxes of paper were shipped weighing 1410 pounds altogether. Write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you use to write the system. (Write System of Equations from Context) !100 POINTS!

Answer 1

First part of the question:

Let x be the number of small boxes and y be the number of large boxes.

According to the first statement, a total of 24 boxes were shipped

=> x+y=24 ---- (Eq.1)

=> x = 24-y --- (Eq.2)

According to 2nd statement, Total weight was 1410 and we know the weight of one small box is 45 and large box is 75.

Therefore,

45x+75y=1410 --- (Eq.3)

Now, using the substitution method for solving the equation,

From equation 1,

$x + y = 24$

$= > x = 24 - y$

Now putting Eq. 3 values,

$45x + 75y = 1410$

$= > 45(24 - y) + 75y = 1410$

$= > 1080 - 45y + 75y = 1410$

$= > - 45y + 75y = 1410 - 1080$

$= > 30y = 330$

$= > y = \frac{330}{30}$

$= > y = 11$

Now putting value of y in Eq.2,

$= > x = 24 - y$

$= > x = 24 - 11$

$= > x = 13$

Therefore,

Number of small boxes shipped=x=13

Number of large boxes shipped=y=12

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Second part of question:

Define the variables that you use to write the system.

Ans:

x is used as a variable to show the number of small boxes.

y is used as a variable to show the number of large boxes.