Answer:
Large box weight = 18.5 kilograms
Small box weight = 15.75 kilograms
Explanation:
We can determine the weight of both types of boxes using a system of equations, where
- l refers to the weight of the large boxes,
- and s refers to weight of the small boxes.
First equation:
Since 5 large boxes and 6 small boxes has a total weight of 187 kilograms, our first equation is given by:
5l + 6s = 187
Second equation:
Since 3 large boxes and 2 small boxes has a total weight of 87 kilograms, our second equation is given by:
3l + 2s = 87
Method to solve: Elimination:
We can solve the system using elimination.
First, we can multiply the second equation by -3, which will allow us to eliminate s since 6s - 6s = 0:
-3(3l +2s = 87)
-9l - 6s = -261
Eliminating s and solving for l:
Now we can add this equation to the first equation, which will allow us to eliminate s and solve for l, the weight of each large box:
5l + 6s = 187
+
-9l - 6s = -261
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(5l - 9l) + (6s - 6s) = (187 - 261)
(-4l = -74) / -4
l = 18.5
Thus, each large box weighs 18.5 kilograms.
Solving for s:
Now we can solve for s by plugging in 18.5 for l in the first equation:
5(18.5) + 6s = 187
(92.5 + 6s = 187) - 92.5
(6s = 94.5) / 6
s = 15.75
Thus, each small box weighs 15.75 kilograms.