A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 25 books and each large box can hold 40 books. A total of 7 boxes were sent which can hold 250 books altogether. Write a system of equations that could be used to determine the number of small boxes sent and the number of large boxes sent. Define the variables that you use to write the system.
Sure, let's define the variables to represent the number of small boxes and large boxes as follows:
Let x be the number of small boxes.
Let y be the number of large boxes.
Based on the given information, we can set up the following system of equations:
Equation 1: The total number of books in the small boxes
25x
Equation 2: The total number of books in the large boxes
40y
Equation 3: The total number of boxes
x + y = 7
Equation 4: The total number of books in all boxes
25x + 40y = 250
So, the system of equations is:
25x + 40y = 250
x + y = 7
Let's define the variables used in the system as follows:
Let "x" represent the number of small boxes sent.
Let "y" represent the number of large boxes sent.
From the given information, we can form the following two equations:
Equation 1: The total number of small boxes times the capacity of each small box (25) should equal the total number of books that fit in small boxes. Therefore, the equation is:
x * 25 = (number of books in small boxes)
Equation 2: The total number of large boxes times the capacity of each large box (40) should equal the total number of books that fit in large boxes. Therefore, the equation is:
y * 40 = (number of books in large boxes)
Additionally, we know that the total number of boxes sent is 7:
x + y = 7
To summarize, the system of equations is:
x * 25 = (number of books in small boxes)
y * 40 = (number of books in large boxes)
x + y = 7
To solve this problem, let's define the variables:
Let's say the number of small boxes sent is S, and the number of large boxes sent is L.
We can set up the following system of equations:
Equation 1: The total number of small boxes and large boxes sent is 7.
S + L = 7
Equation 2: Each small box can hold 25 books, so the total number of books in small boxes is 25S.
Each large box can hold 40 books, so the total number of books in large boxes is 40L.
The total number of books altogether in the sent boxes is 250.
25S + 40L = 250
So, the system of equations is:
S + L = 7
25S + 40L = 250
L = Large boxes
S = Small boxes
Each small box can hold 25 books and each large box can hold 40 books which can hold 250 books altogether:
40 L + 25 S = 250
A total of 7 boxes:
L + S = 7
Your system is:
40 L + 25 S = 250
L + S = 7
______________
By the way the solutions are:
L = 5 , S = 2