A newspaper carrier has $4.90 in change. He has five more quarters than dimes, but two times as many nickles as quarters. How many coins of each type does he have?
x = number of dimes
x + 5 = number of quarters {he has five more quarters than dimes} 2(x + 5) = number of nickels {he has two times as many nickels as quarters} 0.1x + 0.25(x + 5) + 0.05(2x + 10) = 4.9 {value of coin times number of coins equals total value} 0.1x + 0.25x + 1.25 + 0.1x + 0.5 = 4.9 {used distributive property} 0.45x + 1.75 = 4.9 {combined like terms} 0.45x = 3.15 {subtracted 1.75 from each side} x = 7 {divided each side by 0.45} x + 5 = 12 {substituted 7, in for x, into (x + 5)} 2(x + 5) = 24 {substituted 7, in for x, into 2(x + 5)} 7 dimes 12 quarters 24 nickels Ask Algebra House Comments are closed.

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