Question

Can you please help on this Algebra problem?
Keana's piggy bank contains $4.30 in nickels and dimes only. If she has 59 coins in her ban, 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.

I have so far:
n = number of nickels
d = number of dimes
n+d = 430
5n + 10d = 430

But I am not sure what step is next to figure out how to solve for nickels only. Thank you

Answer 1

first of all just divide the 2nd equation by 5 to get
n + 2d = 86, the other is
n + d = 59 <<---- you had 430 here.
subtract them:
d = 27
then in n+d = 59 , n+27 = 59
n = 32

She has 27 dimes and 32 nickels


check:
is 27+32 = 59 for the sum of coins? YES
for the value of coins, is
27(10) + 32(5) = 430 ?, YES

My answer is correct.