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.

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10-12-2016
Mathematics

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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.

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Аноним Аноним · Answer 1 · 2016-12-13T09:14:49+01:00

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