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Scorpion4ik [409]
3 years ago
12

A fruit company delivers its truit in two type of boxes: large and small. A delivery of 3 large boxes and 2 small boxes has a to

tal weight of 86 kilograms. A delivery of 8 large boxes and 4 small boxes has a total weight of 209 kilograms . How much does each type of box weight?
Mathematics
1 answer:
Ronch [10]3 years ago
8 0

Answer:

Large box: 18.5\ kilograms

Small box: 15.25\ kilograms

Step-by-step explanation:

Let be "l" the weight in kilograms of a large box and "s" the weight in kilograms of a smalll box.

Set up a system of equations:

\left \{ {{3l+2s=86} \atop {8l+4s=209}} \right.

In order to solve the system of equations, you can apply the Elimination Method. Multiply the first equation by -2, add the equations and then solve for "l":

\left \{ {{-6l-4s=-172} \atop {8l+4s=209}} \right.\\......................\\2l=37\\\\l=\frac{37}{2}\\\\l=18.5

Finally, susbstitute the value of "l" into any original equation and solve for "s":

3(18.5)+2s=86\\\\2s=86-55.5\\\\s=\frac{30.5}{2}\\\\s=15.25

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One nice thing about this situation is that you’ve been given everything in the same base. To review a little on the laws of exponents, when you have two exponents with the same base being:

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Putting those both into our first question gives us -6 1/2 - (-6 1/2), which is 0, since any number minus itself gives us 0.

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