Question 1208347
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last Christmas, Angel was able to collect 12 bills consisting of 20 bills and 50 bills 
form her titas and titos. She received a total bill of 390 from them, 
How many of each bill did Angel received? Using trial and error
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            I  will apply "smart trial and error", 

        in distinction from stupid trial and error.



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Let assume first that all 12 bills were 20-bills.

Then the total would be 12*20 = 240 monetary units.


         But Angel collected 390 monetary units, 
    and the difference is 390-240= 150 monetary units.


It means that not all 12 bills were 20-bills - some were 50-bills.


When we mentally replace 20-bill by 50-bill in our head, we add 50-20 = 30 monetary units.


Hence, in order for to compensate the 150 monetary difference, 
we should make  {{{150/30}}} = 5 replacement.


It tells us that in the real collection Angel had 5 50-bills.
The rest were 12-5 = 7 20-bills.


<U>ANSWER</U>.  In her collection, Angel had 7 20-bills and 5 50-bills.


<U>CHECK</U>.  7*20 + 5*50 = 140 + 250 = 390,  total value.    ! correct !
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Solved.