Question

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.

Answer 1

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