Socrates - Comenius 1: |
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Mathematics
Second task
14 tons of ore were delivered to the smelting works. The pure metal and the alloys were supplied in it in the ratio 2 : 5. In the raw cast obtained by smelting the ore, this ratio changed to 24 : 1 for the benefit of the ore. How many kilos did the cast weigh if the loss of metal during the smelting process made 5 %?
Solution:
14 tons = 14000 kilos of ore were delivered.
In the ore, the pure metal and the alloy are supplied in the ratio 2 : 5, i. e. there are two parts of the metal; one part weighs 14000 kg : 7 = 2000 kg, two parts weigh 4000 kg.
In the raw cast, the metal loss is 5 %, i. e. the metal mass is 0.95 . 4000 kg = 3800 kg.
We can reckon the cast mass using rule of three:
24 parts …………………….. 3800 kg |
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25 parts ……...…..………………. x kg |
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25 : 24 |
= |
x : 3800 |
x |
= |
(3800 . 25) : 24 |
x |
= |
3958.3 kg |
The cast weighed about 3958.3 kg.