A fruit company packages its fruit into two types of boxes: large and small. This morning, the company made two deliveries. The table below shows the number of boxes in each delivery and the total weight (in kilograms).
First delivery Second delivery
Number of 2 4
large boxes
Number of 3 8
small boxes
Total weight 50 113
(in kilograms)
Let be the weight (in kilograms) of each large box.
Let be the weight (in kilograms) of each small box.
(a) Write a system of equations that could be used to find the weight (in kilograms) of each
type of box.
(b) How much does each type of box weigh (in kilograms)?
(a) We can set up the following system of equations:
2L + 3S = 50
4L + 8S = 113
Where L represents the weight of each large box and S represents the weight of each small box.
(b) To solve the system of equations, we can use elimination or substitution.
Let's use elimination. We multiply the first equation by 4 and the second equation by 2, then subtract the second equation from the first:
8L + 12S = 200
-(8L + 16S = 226)
------------------
-4S = -26
Dividing both sides of the equation by -4, we find that S = 26/4 = 6.5.
Substituting this value of S into the first equation, we can solve for L:
2L + 3(6.5) = 50
2L + 19.5 = 50
2L = 50 - 19.5
2L = 30.5
L = 30.5/2
L = 15.25
Therefore, each large box weighs 15.25 kilograms and each small box weighs 6.5 kilograms.