Ask Question
11 June, 16:39

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 3 large boxes and 5 small boxes has a total weight of 112 kilograms. A delivery of 6 large boxes and 2 small boxes has a total weight of 118 kilograms. How much does each type of box weigh?

+5
Answers (1)
  1. 11 June, 18:35
    0
    Let's call the weight of the large boxes:

    l

    Let's call the weight of the small boxes:

    s

    From the information in the equation we can now write two equations:

    Equation 1:

    5

    l

    +

    3

    s

    =

    99

    Equation 2:

    7

    l

    +

    9

    s

    =

    171

    Step 1) Solve each equation for

    9

    s

    :

    Equation 1:

    5

    l

    +

    3

    s

    =

    99

    5

    l

    -

    5

    l

    +

    3

    s

    =

    99

    -

    5

    l

    0

    +

    3

    s

    =

    99

    -

    5

    l

    3

    s

    =

    99

    -

    5

    l

    3

    *

    3

    s

    =

    3

    (

    99

    -

    5

    l

    )

    9

    s

    =

    (

    3

    *

    99

    )

    -

    (

    3

    *

    5

    l

    )

    9

    s

    =

    297

    -

    15

    l

    Equation 1:

    7

    l

    +

    9

    s

    =

    171

    7

    l

    -

    7

    l

    +

    9

    s

    =

    171

    -

    7

    l

    0

    +

    9

    s

    =

    171

    -

    7

    l

    9

    s

    =

    171

    -

    7

    l

    Step 2) Because the left side of both equations are equivalent or the same we can equate the right side of each equation and solve for

    l

    :

    297

    -

    15

    l

    =

    171

    -

    7

    l

    297

    -

    171

    -

    15

    l

    +

    15

    l

    =

    171

    -

    171

    -

    7

    l

    +

    15

    l

    126

    -

    0

    =

    0

    +

    (

    -

    7

    +

    15

    )

    l

    126

    =

    8

    l

    126

    8

    =

    8

    l

    8

    15.75

    =

    8

    l

    8

    15.75

    =

    l

    l

    =

    15.75

    Step 3) Substitute

    15.75

    for

    l

    in the solution to either equation in Step 1 and solve for

    s

    :

    9

    s

    =

    297

    -

    15

    l

    becomes:

    9

    s

    =

    297

    -

    (

    15

    *

    15.75

    )

    9

    s

    =

    297

    -

    236.25

    9

    s

    =

    60.75

    9

    s

    9

    =

    60.75

    9

    9

    s

    9

    =

    6.75

    s

    =

    6.75

    The Solution Is:

    The large boxes weigh 15.75 Kg

    The small boxes weigh 6.75 Kg
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 3 large boxes and 5 small boxes has a total weight ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers