Question

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 5 large boxes and 3 small boxes has a total weight of 131 kilograms. A delivery of 2 large boxes and 6 small boxes has a total weight of 116 kilograms. How much does each type of box weigh?

Answer 1

• large: 18.25 kg
• small: 13.25 kg

Explanation:

A graphical solution works nicely for this.

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The relevant equations are (for large box weight x and small box weight y in kilograms) ...

• 5x +3y = 131
• 2x +6y = 116

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A system of linear equations can be solved by a variety of methods. In most cases, a graphing calculator can give a quick and easy solution.

Here, we'll also use Cramer's rule for the solution. It gives the answers with combinations of the coefficients and constants substantially equivalent to solution by "elimination."

x = (3·116 -6·131)/(3·2 -6·5) = -438/-24 = 18.25

y = (131·2 -116·5)/-24 = -318/-24 = 13.25

Then the answers are ...

• the large box weighs 18.25 kg
• the small box weighs 13.25 kg

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Since all the numbers in these equations are different, you can see the pattern of multiplication and subtraction that we used to get the solution. That same pattern can be applied to any linear system of 2 equations in 2 unknowns.

Answer 2

The weight of large and small box are 18.25 kg and 13.25 kg respectively.

Explanation:

Let the weight of large and small box are x and y respectively.

It is given that a delivery of 5 large boxes and 3 small boxes has a total weight of 131 kilograms.

`5x+3y=131` .... (1)

A delivery of 2 large boxes and 6 small boxes has a total weight of 116 kilograms.

`2x+6y=116` .... (2)

On solving (1) and (2) using graphing calculator, we get

`x=18.25`

`y=13.25`

Therefore the weight of large and small box are 18.25 kg and 13.25 kg respectively.