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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.
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 = 5 replacement.
It tells us that in the real collection Angel had 5 50-bills.
The rest were 12-5 = 7 20-bills.
ANSWER. In her collection, Angel had 7 20-bills and 5 50-bills.
CHECK. 7*20 + 5*50 = 140 + 250 = 390, total value. ! correct !
Solved.