COINS~word problem

[emmaiskool242]

Marvella has 23 coins in nickels,dimes, and quarters. If she has twice as many nickels as dimes and has $2.45, how many of each does she have?

Well I tried like three times to set up this problem and I couldn't figure out exactly how to do it, so if you could show me how to set it up I could probaly figure it out~thanks

 

[tkhunny]

What did you try? Let's see how close you get.

 

[emmaiskool242]

So I tried setting it up like 2n=d, d+n+q=23 so then you would put....2n+n+q=23,3n+q=23,but how you would solve that?

So then I tried doing this~2(0.05n)+0.05n+0.25q=$2.45. But that doesn't make much sense either.

So then I figure to solve it, I think it has to be some combination of the both...

So thats what I did...neither make much sense but I tried


Could you help me?

 

[pka]

\(\displaystyle \L
\begin{array}{r}
n + d + q = ? \\
.05n + .10d + .25q = ? \\
n = 2d \\
\end{array}\)

 

[Denis]

"So I tried setting it up like 2n=d, d+n+q=23 so then you would put....2n+n+q=23,3n+q=23,but how you would solve that?"

Well start by being CAREFUL: n = 2d ; NOT 2n = d;
that'll result in 3d + q = 23, so q = 23 - 3d [1]

"So then I tried doing this~2(0.05n)+0.05n+0.25q=$2.45. But that doesn't make much sense either."

you have 2d nickels, so .05(2d)
you have d dimes, so .10(d)
you have q quartwes, so .25(q)

.05(2d) + .10(d) + .25(q) = 2.45
.20d + .25q = 2.45 ; make it easier by multiplying by 100:
20d + 25q = 245 ; simplify by dividing by 5:
4d + 5q = 49 [2]

Now substitute [1] in [2] and solve for d

 

[emmaiskool242]

wow thanks for the help i'm going to try that =)