Coin Problem

​Mark has a total of 41 coins consisting of nickels and quarters the total value of the coins is $4.85. How many of each type of coin does he have? 

x = number of nickels 
41 - x = number of quarters   {there are a total of 41 coins} 

.05x + .25(41 - x) = 4.85   {value of coin times number of coins equals total value} 
.05x + 10.25 - .25x = 4.85   {used distributive property} 
-.02x + 10.25 = 4.85   {combined like terms} 
-.02x = -5.4   {subtracted 10.25 from each side} 
x = 27   {divided each side by -.02} 
41 - x = 14   {substituted 27, in for x, into 41 - x} 

27 nickels and 14 quarters

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