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? 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 © Algebra House
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