Socrates - Comenius 1: 
School Project “We are all living under the same sky”


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

25 parts ……...…..………………. x kg

__________________________________

25 : 24

=

x : 3800

x

=

(3800 . 25) : 24

x

=

3958.3 kg

The cast weighed about 3958.3 kg.