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?

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