SOLUTION: A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 6 large boxes and 5 small boxes has a total weight of 145 kilograms. A delivery of 2 large
Question 1144628: A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 6 large boxes and 5 small boxes has a total weight of 145 kilograms. A delivery of 2 large boxes and 3 small boxes has a total weight of 57 kilograms. How much does each type of box weigh? Found 2 solutions by ikleyn, josgarithmetic:Answer by ikleyn(52809) (Show Source):
Without any explanations, it is clear that from the condition you have these 2 equations in 2 unknowns
6x + 5y = 145 kilograms (1)
2x + 3y = 57 kilograms (2)
To solve it, use Elimination method.
For it, multiply equation (2) by 3 (both sides). Keep equation (1) as is
6x + 5y = 145 (1')
6x + 9y = 171 (2')
From equation (2') subract equation (1'). The terms " 6x " will cancel each other, and
you will get one single equation for "y"
9y - 5y = 171 - 145, or
4y = 26
y = 26/4 = 6.5.
Thus small box weights 6.5 kilograms.
Now substitute it into equation (2) to find "x" :
2x + 3*6.5 = 57,
2x = 57 - 3*65 = 37.5.
x = 37.5/2 = 18.75.
ANSWER. Large box weights 18.75 kilograms. Small box weights 6.5 kilograms.
CHECK. Equation (1) : 6*18.75 + 5*6.5 = 145 kilograms. ! Correct !
Equation (2) : 2*18.75 + 3*6.5 = 57 kilograms. ! Correct !
Solved.
On the way, you learned on how the Elimination method works.
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