Question

A woman has $1.70 in dimes and nickels. She has 2 more dimes than nickels. How many nickels does she have?

Answer 1

10 nickels and 12 dimes

1) We can solve this by writing equations. So let's do it considering that:

`\begin{gathered} 1d=\$0.10 \\ 1n=\$0.05 \end{gathered}`

2) So we can write out the quantities in cents, so 5 cents = 1 nickel and 10 cents one dime, and $1.70 = 170 cents:

5n+10d=170

d=n+2

So let's solve this system of Linear Equations by the Substitution Method:

`\begin{gathered} 5n+10d=170 \\ d=n+2 \\ 5n+10(n+2)=170 \\ 5n+10n+20=170 \\ 15n+20=170 \\ 15n=170-20 \\ 15n=150 \\ (15n)/(15)=(150)/(15) \\ n=10 \end{gathered}`

Now, let's plug into the equation the number of nickels to find the number of dimes that woman has:

`\begin{gathered} d=n+2 \\ d=10+2 \\ d=12 \end{gathered}`

3) So, we can state that the answer is: 10 nickels and 12 dimes