Keana’s piggy bank contains $4.30 in nickels and dimes only. if she has 59 coins in her bank, then what is the sum of the digits in the number of nickels in keana’s bank? write a system of equations for this situation and find its solution.

n = number of nickels
d = number of dimes 

n + d = 59   {she has 59 coins total}
5n + 10d = 430   {value of coin times number of coins equals total value} 

-5n - 5d = -295   {multiplied top equation by -5}
5n + 10d = 430   {bottom equation stays the same}

5d = 135   {added the two equations}
d = 27   {divided each side by 5} 

n + d = 59   {first original equation}
n + 27 = 59   {substituted 27, in for d, into first original equation}
n = 32   {subtracted 27 from each side} 

27 dimes 
32 nickels

To answer the question, "what is the sum of the digits in the number of nickels?",
add 3 + 2
= 5

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