Question 1189814
A fruit company delivers its fruit in two types of boxes: large and small.
 A delivery of 3 large boxes and 8 small boxes has a total weight of 91 kilograms
 delivery of 5 large boxes and 2 small boxes has a total weight of 78 kilograms.
 How much does each type of box weigh?
:
let a = weight of the large box
let b = weight of the small
:
 "A delivery of 3 large boxes and 8 small boxes has a total weight of 91 kg"
3a + 8b = 91
 "delivery of 5 large boxes and 2 small boxes has a total weight of 78 kg."
5a + 2b = 78
:
 How much does each type of box weigh?
multiply the above equation by 4, subtract the first equation
20a + 8b = 312
 3a + 8b = 91
----------------subtraction eliminates b, find a
17a + 0 = 221
a = 221/17
a = 13 kg each large box
:
 use the 2nd equation to find b
5(13) + 2b = 78
65 + 2b = 78
2b = 78 - 65
2b = 13
b = 13/2
b = 6.5 kg each small box
:
:
Check solutions in the 1st equation
3(13) + 8(6.5) =
39 + 52 = 91