SOLUTION: A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 6 large boxes and 5 small boxes has a total weight of 145 kilograms. A delivery of 2 large

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Question 1144628: A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 6 large boxes and 5 small boxes has a total weight of 145 kilograms. A delivery of 2 large boxes and 3 small boxes has a total weight of 57 kilograms. How much does each type of box weigh?
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52810)   (Show Source): You can put this solution on YOUR website!
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Without any explanations, it is clear that from the condition you have these 2 equations in 2 unknowns


    6x + 5y = 145   kilograms     (1)

    2x + 3y =  57   kilograms     (2)


To solve it, use Elimination method.

For it, multiply equation (2) by 3 (both sides).  Keep equation (1) as is


    6x + 5y = 145                 (1')

    6x + 9y = 171                 (2')


From equation (2') subract equation (1').  The terms  " 6x " will cancel each other, and

you will get one single equation for "y"


    9y - 5y = 171 - 145,   or

    4y       = 26

     y       = 26/4 = 6.5.


Thus small box weights 6.5 kilograms.

Now substitute it into equation (2) to find "x" :


    2x + 3*6.5 = 57,

    2x = 57 - 3*65 = 37.5.

     x             = 37.5/2 = 18.75.


ANSWER.  Large box weights  18.75 kilograms.  Small box weights  6.5 kilograms.


CHECK.  Equation (1) :  6*18.75 + 5*6.5 = 145 kilograms.   ! Correct !

        Equation (2) :  2*18.75 + 3*6.5 = 57 kilograms.   ! Correct !

Solved.

On the way, you learned on how the Elimination method works.

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On solving systems of linear equations in two unknowns see the lessons
    - Solution of a linear system of two equations in two unknowns by the Substitution method
    - Solution of a linear system of two equations in two unknowns by the Elimination method
    - Solution of a linear system of two equations in two unknowns using determinant
    - Geometric interpretation of a linear system of two equations in two unknowns
    - Useful tricks when solving systems of 2 equations in 2 unknowns by the Substitution method
    - Solving word problems using linear systems of two equations in two unknowns

    - Oranges and grapefruits
    - Using systems of equations to solve problems on tickets
    - Three methods for solving standard (typical) problems on tickets
    - Using systems of equations to solve problems on shares
    - Using systems of equations to solve problems on investment
    - Two mechanics work on a car
    - The Robinson family and the Sanders family each used their sprinklers last summer
    - Roses and vilolets
    - Counting calories and grams of fat in combined food
    - A theater group made appearances in two cities
    - HOW TO algebreze and solve this problem on 2 equations in 2 unknowns
    - One unusual problem to solve using system of two equations
    - Solving mentally word problems on two equations in two unknowns
in this site. They all are free of charge.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Systems of two linear equations in two unknowns".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
x small box weigh
y large box weight







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