SOLUTION: A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 3 large boxes and 2 small boxes has a total weight of 69 kilograms. A delivery of 5 large b

Question 1111852: A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 3 large boxes and 2 small boxes has a total weight of 69 kilograms. A delivery of 5 large boxes and 6 small boxes has a total weight of 133 kilograms. How much does each type of box weigh?
weight of each large box:____ kilograms
weight of each small box:____ kilograms

Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
large box x kg
small box y kg
Equation for tickets total distance

3 x + 2 y = 69 .............1

Equation for amount spent
5 x + 6 y = 133 .............2
Eliminate y
multiply (1)by 3.00
Multiply (2) by -1
9.00 x 6.00 y = 207.00
-5.00 -6.00 y = -133.00
Add the two equations
4.00 x = 74.00
/ 4.00
x = 18.50
plug value of x in (1)
3.00 x + 2.00 y = 69.00
55.50 + 2.00 y = 69.00
2.00 y = 13.50
y= 6.75

large box 18.50 kg
small box 6.75 kg
m.ananth@hotmail.ca

Answer by ikleyn(52903)   (Show Source): You can put this solution on YOUR website!
.
The solution and the answers by @mananth were   W R O N G.

3x + 2y = 69, (1) 5x + 6y = 133. (2) Apply the Elimination method. For it, multiply eq(1) by 3. Keep eq(2) as is: 9x + 6y = 207, (1') 5x + 6y = 133. (2') Subtract eq(2') from eq(1'). You will get 9x - 5x = 207 - 133 4x = 74. ====> x = = 18.5. Then from eq(1) 3*18.5 + 2y = 69 ====> 2y = 69 - 3*18.5 = 13.5 ====> y = = 6.75. Answer. Large box weights 18.5 kg. Small box weights 6.75 kg. Check. 3*18.5 + 2*6.75 = 69. ! Correct ! 5*18.5 + 6*6.75 = 133. ! Correct !

Solved correctly.

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