Loose change question

Valerie checked her loose change jar recently, and figured out that she had enough dimes and quarters to make a total of $11.55, and that the number of quarters was six less than half the number of dimes. How many of each coin does she have? 

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x = number of dimes
0.5x - 6 = number of quarters   {quarters was six less than half the dimes}

10x + 25(0.5x - 6) = 1155   {number of coins times value of coin equals total value}
10x + 12.5x - 150 = 1155   {used distributive property}
22.5x - 150 = 1155   {combined like terms}
22.5x = 1305   {added 150 to both sides}
x = 58   {divided both sides by 22.5}
0.5x - 6 = 23   {substituted 58 in for x}

58 dimes and 23 quarters 

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