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12375819
14.11.2019 •
Mathematics
Afruit company delivers its fruit in two types of boxes: large and small. a delivery of 2 large boxes and 5 small boxes has a total weight of 77 kilograms. a delivery of 8 large boxes and 3 small boxes has a total weight of 104 kilograms. how much does each type of box weigh?
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Ответ:
The answer is that large boxes are 8.5 kilograms and small boxes are 12 kilograms.
Step-by-step explanation:
Let l = large boxes and s = small boxes.
Delivery 1:
2 large boxes plus 5 small boxes = 77 kilograms
2l + 5s = 77 kilograms
The 8 large boxes plus 3 small boxes = 104 kilograms
8l + 3s = 104 kilograms
Solve for l:
8l = -3s + 104
l = -3/8s + 104/8
l = -3/8s + 13
Substitute:
2l + 5s = 77
2(-3/8s + 13) + 5s = 77
-6/8s + 26 + 5s = 77
--6/8s + 5s = 77 - 26
-6/8s + 40/8s = 51
34/8s = 51
s = 51 * 8/34 = 408/34 = 12 kilograms for small boxes
l = -3/8s + 13 = -3/8(12) + 13 = -36/8 + 104/8 = 68/8 = 8.5 kilograms
Proof 1:
8l + 3s = 104
8(8.5) + 3(12) = 104
68 + 36 = 104
104 = 104
Proof 2:
2l + 5s = 77
2(8.5) + 5(12) = 77
17 + 60 = 77
77 = 77
Hope this helps! Have a great day!
Ответ:
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Step-by-step explanation: