Question

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 

3

 large boxes and 

2

 small boxes has a total weight of 

54

 kilograms. A delivery of 

5

 large boxes and 

6

 small boxes has a total weight of 

108

 kilograms. How much does each type of box weigh?

Answer 1

The answers are

large box - 13.5

small box- 6.75

Explanation:

systems of equations

Answer 2

A fruit company delivers fruits
=> 3 large boxes and 2 small boxes weighs = 54 kilograms
=> 5 large boxes and 6 small boxes weighs = 108 kilograms
Now, let’s find how does each type of box weigh
=> 3a + 2b = 54, where a and b are the unknown weights of each boxes
=> 5a + 6b = 108
Multiply the first given equation by 3 on both side to cross out letter B and find the value of A.
=> 3a(3) + 2b(3) = 54(3)
=> 9a + 6B = 162
Now subtract this by the second equation:
=> 9a + 6B = 162 – 5a + 6b =106
=> 4a = 56
=> 4a / a =56 /4
=> a = 14 – The weight of large boxes
Now, let’s find the B
=> 3(14) + 2b = 54
=> 42 + 2b = 54
=> 2b = 54 – 42
=> 2b = 12
=> 2b/2= 12/2
=> b = 6 = the weight of small boxes