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)}

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 nickels12 quarters

24 nickels

**- Algebra House**