Nickels and Dimes

[stephanie953]

Candice paid her library fine of $0.80 with 10 coins consisting of nickels and dimes. How many of each coin did she use?

I though x would represent nickels and dimes would be 2x.

x + 2x = 80
That didnt work.
5(x) + 10 (2x) = 80
That doesnt either
Then I thought maybe

5(x) + 5 (2x) = 80
5x + 10x
Doesn't work.

What am I missing? Thank you!

 

[galactus]

No 2x necessary. 10 is already twice 5. Try this:

\(\displaystyle \L\\x+y=10\)
\(\displaystyle \L\\5x+10y=80\)

 

[stephanie953]

Do I leave it as is or is there a way to determine what x & y are? I believe it is 6 dimes and 4 nickels, but I don't know how to solve it completely with an algebraic equation. Thank you so much for the response.

 

[Denis]

What grade are you in, Stephanie?

x + y = 10; then x = 10 - y : understand that?

If so, substitute in 5x + 10y = 80;
if not, see your math teacher.

 

[stephanie953]

Thanks for the reply. Now that I see it I understand. Sometimes it takes a moment for it to click in.