SOLUTION: Jonathan finds 52 cents in his car consisting of pennies, nickels, and dimes. He finds 2 more nickels than dimes, and three times as many pennies as nickels. How many of each coin
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Question 1058874: Jonathan finds 52 cents in his car consisting of pennies, nickels, and dimes. He finds 2 more nickels than dimes, and three times as many pennies as nickels. How many of each coin does he find? Answer by ikleyn(52777) (Show Source):
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Jonathan finds 52 cents in his car consisting of pennies, nickels, and dimes. He finds 2 more nickels than dimes,
and three times as many pennies as nickels. How many of each coin does he find?
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For a moment, put aside 2 nickels and 6 pennies (mentally).
Then the remained coins worth is 52 - 2*5 - 6 = 36 cents.
Now you can group the rest of the coins in sets containing {1 nickel, 1 dime, 3 pennies} each.
Each set worth is 5 + 10 + 3 = 18 cents.
How many such sets are there among remained coins? = 2.
Now return back that coins you put aside at the beginning.
Answer. 2+2 = 4 nickels, 2 dimes and 3*2+6 = 12 pennies were there in the collection.
This method allows to solve the problem without using equations.
