Question 1209934
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Here is a quick and easy informal mental solution to the problem.<br>
The combined wages of 7 technicians and 3 apprentices is 820.
When one apprentice becomes a technician, the combined wages of 8 technicians and 2 apprentices is 880.
So when an apprentice becomes a technician, the combined wages go up by 60.<br>
Have that happen twice more, ending up with 10 technicians and 0 apprentices.  The combined wages is now 880 + 60 + 60 = 1000.<br>
So the wage for each technician is 1000/10 = 100.<br>
When there were 7 technicians and 3 apprentices, the total wages was 820.  The wages for the 7 technicians was 7*100 = 700, so the wages for the 3 apprentices was 820-700 = 120; so the wage for each apprentice is 120/3 = 40.<br>
Alternatively, once we find that the wages for each technician is 100, we can use the fact that the total wages increase by 60 each time an apprentice becomes a technician to determine that the wage for each apprentice is 100-60 = 40.<br>