A moving Company weighs 20 boxes you have packed that contain either books or clothes and says the total weight is 404 pounds. You know that a box of books weighs 40 pounds and a box of clothes weighs 7 pounds. Find how many boxes of books and how many boxes of clothes you packed.
number of boxes of books ---> x
number of boxes of clothing ---> 20-x
solve
40x + 7(20-x) = 404
To solve this problem, we need to set up a system of equations based on the given information.
Let's say the number of boxes containing books is 'b', and the number of boxes containing clothes is 'c'.
We know that each box of books weighs 40 pounds, so the total weight of the book boxes is 40b. Similarly, each box of clothes weighs 7 pounds, so the total weight of the clothes boxes is 7c.
According to the information provided, the total weight of all the boxes is 404 pounds. Therefore, the equation becomes:
40b + 7c = 404
Additionally, we know that the total number of boxes is 20. Hence, we have another equation:
b + c = 20
Now we have a system of two equations:
40b + 7c = 404,
b + c = 20.
To solve this system, we can use the method of substitution or elimination.
Method 1: Substitution
From the second equation, we can rewrite it as b = 20 - c.
Substituting this value of b into the first equation, we get:
40(20 - c) + 7c = 404.
Expanding the equation, we have:
800 - 40c + 7c = 404.
800 - 33c = 404.
-33c = -396.
c = 12.
Now substitute the value of c back into the equation b + c = 20:
b + 12 = 20,
b = 20 - 12,
b = 8.
Therefore, you packed 8 boxes of books and 12 boxes of clothes.
Method 2: Elimination
Multiply the second equation by 40 to make the coefficients of b in both equations equal:
40b + 40c = 800.
Now subtract this equation from the first equation:
(40b + 7c) - (40b + 40c) = 404 - 800,
-33c = -396,
c = 12.
Substitute this value of c back into the equation b + c = 20:
b + 12 = 20,
b = 20 - 12,
b = 8.
So, you packed 8 boxes of books and 12 boxes of clothes.