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A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 5 large boxes and 6 small boxes has a total weight of 187 kilograms. A delivery of 3 large boxes and 2 small boxes has a total weight of 87 kilograms. How much does each type of box weigh?

 Mar 15, 2020
 #1
avatar+44 
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You could say that one large box is x and one small box is y.

 

So, 5x+6y=187

3x+2y=87

 

You could first solve for x (large box)

 

Find the LCM of 6 and 2 (6)

 

5x+6y=187

9x+6y=261

 

261-187=74

4x=74

74/4=18.5(for large box)

 

Now for the small box.

 

Find the LCM of 3 and 5 (15)

 

15x+18y=561

15x+10y=435

 

561-435=126

8y=126

126/8=15.75(small box)

(all answers are in kg)

cool

 Mar 15, 2020
edited by TheGreatestOofman  Mar 15, 2020
 #2
avatar+21827 
+1

5 l + 6 s = 187

3 l + 2 s = 87           multiply this equation by -3

-9 l - 6 s = -261       add top and bottom equations

-4 l = -74

l = 18.5 kg           3(18.5) + 2s = 87      s = 15.75 kg

 Mar 15, 2020

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