Question

Your piggy bank has 50 coins worth a total of $4.55. The coins are only nickels and dimes. How many coins are nickels, how many are dimes?

Answer 1

N= number of nickels

D= number of dimes

from the part of the question that says: "Your piggy bank has 50 coins" we know that N+D=50

and from the part that says: "worth a total of $4.55" and since the nickel is $0.05 and the dime is $0.10 then 0.05N+0.10D=4.55

now we have a system of two equations, let's solve it:

1. multiply the first equation by -0.05, obtaining

`-0.05N-0.05D=-2.5`

2. add the previous equation to the second one:

`0.05D=2.05`
`D=(2.05)/(0.05)=41`

then there will be 41 dimes in the piggy bank, and replacing D for this value in the first equation, we obtain that N=9 then there will be 9 nickels in the piggy bank: