Coin Problem

Lauren has a total of two hundred seventy pennies, nickels, and quarters. She has a total of $17.10. She has two times as many nickels as quarters and one-third as many quarters as pennies. How many of each coin does she have?

x = number of quarters
2x = number of nickels   {two times as many nickels as quarters}
3x = number of pennies   {one-third as many quarters as pennies}

0.25x + 0.05(2x) + 0.01(3x) = 17.10    {number of coins times value of coin equals total value}
0.25x + 0.1x + 0.03x = 17.1   {multiplied through}
0.38x = 17.1   {combined like terms}
x = 45 quarters   {divided each side by 0.38}
2x = 90 nickels   {substituted 45 for x, into 2x}
3x = 135 pennies   {substituted 45 for x, into 3x} 

45 quarters, 90 nickels, and 135 pennies

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