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# Algebra word problem?

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A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 12 large boxes and 2 small boxes has a total weight of 253 kilograms. A delivery of 3 large boxes and 5 small boxes has a total weight of 133 kilograms. How much does each type of box weigh?

Guest Aug 29, 2017
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Let L  be the weight of the large box and S  be the weight of a small box

So.....we have this system

12L +  2S  = 253

3L  +  5S  = 133

Looking at the second equation  and multiplying both sides by 4, we have that

12L + 20S  = 532

Which implies that   12L  = 532 - 20S

Sub  this expression for 12L  into the first equation and we have

532 - 20S + 2S  = 253     simplify

532 - 18S  = 253           subtract  532 from each side

-18S  = -279     divide both sides by  -18

S =  279/18   = 15.5 kg

And the large box weighs

12L  = 532 - 20 (15.5)

L =   [ 532 - 20(15.5) ] / 12  = 18.5 kg

CPhill  Aug 29, 2017

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