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.

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

Putting the value of x in eqn 2

Putting the value of y in eqn 1

So,

Number of small boxes shipped = 10

Number of large boxes shipped = 12 ..

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,

Now putting Eq. 3 values,

Now putting value of y in Eq.2,

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.

The answer is in the image 

y=2x+15

where y=Value of coin

x=Age in years

Value of coin after 19 years=2*19+15

=$53

Therefore, Value after 19 years=$53

The answer is in the image 

The solution is given in the image below

Speed=Distance/time

Here,

distance=15m

time=1sec

speed=15/1=15m/sec

Distance=Speed*time

time=15min=15*60sec=900sec

Distance travelled in 15 min=15*900=13,500m

=13500/1000 km=13.5Km

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

30% of 420 are first year students

first year students = (30/100 )*420

=126 students

Student who are not in first year = 420-126

=294 students