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

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}

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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**

**- Algebra House**