Question

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 2 large boxes and 12 small boxes has a total weight of 115 kilograms. A delivery of 5 large boxes and 3 small boxes has a total weight of 112 kilograms. How much does each type of box weigh

Answer 1

A large box is 18.5 and small is 15.5

Explanation:

Answer 2

Large box's weight = 18.5 kilogram

small box's weight = 6.5 kilogram

Explanation:

We need to make equation to get the weigh of each box.

Let,

Large box = l

Small box = s

According to the question,

2l + 12s = 115 ........... (i)

Again, 5l + 3s = 112 ........ (ii)

From equation (i), we can say that,

or, 2l = 115 - 12s [changing the side]

or, l =
`(115 - 12s)/(2)` [divide both the sides by 2] ........ (iii)

Putting the value of "l" in equation (ii), we get,

5l + 3s = 112

or, 5 ×
`(115 - 12s)/(2)` + 3s = 112

or,
`(575 - 60s)/(2)` + 3s = 112

or,
`(575 - 60s + 6s)/(2)` = 112

or, 575 - 54s = 112 × 2 [multiplying by 2]

or, 575 - 54s = 224

or, -54s = 224 - 575 [changing the side]

or, -54s = -351

or, s =
`(-351)/(-54)`

or, s = 6.5

Putting the value of "s" in equation (iii),

l =
`(115 - 12*6.5)/(2)`

or, l =
`(115 - 78)/(2)`

or, l = 37 ÷ 2

l = 18.5

Therefore, large box = 18.5 kilogram

small box = 6.5 kilogram