Ricardo Gutierrez has a box of coins that he uses when playing poker with friends. The box currently contains 46 coins, consisiting of pennies, dimes, and quarters. The number of pennies is equal to the number of dimes, and the total value is $4.87. How many of each denomination of coin does he have?
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Let x be the number of pennies.
Since the number of pennies and the number of dimes are equal, x is also the number of pennies.
And 46-(x+x); 46-2x be the number of quarters.
It is already established that the value of pennies is $0.01, dimes $0.10 and quarters $0.25.
(x)(.01)+(x)(.10)+(46-2x)(.25)=4.87 => establishing the equation
(x)(1)+(x)(10)+(46-2x)(25)=487 => mult by 100 to computer easily
11x + 1150 - 50x = 487
663 = 39x
x = 17
All in all, there are 17 pennies, 17 dimes and 46-(2*17); 12 quarters.