Question 808513
THE ALGEBRA WAY:
{{{n}}}= number of nickels
{{{q}}}= number of quarters
 
"I have twice as many nickels as I do quarters" translates into
{{{n=2q}}}

The phrase "together they add up to $4.90" translates into
{{{5n+25q=490}}} if you are thinking in cents, or
{{{0.05n+0.25q=4.90}}} if you are thinking in $.
Needless to say, I like {{{5n+25q=490}}} better,
but we could divide both sides of that equation by 5 and get a simpler equation:
{{{(5n+25q)/5=490/5}}}-->{{{5n/5+25q/5=98}}}-->{{{n+5q=98}}}
From {{{0.05n+0.25q=4.90}}} you could multiply both sides times 20 to get the same result:
{{{20*(0.05n+0.25q)=20*4.90}}}-->{{{20*0.05n+20*0.25q=98}}}}-->{{{n+5q=98}}}
 
You end up with a system of two equations, one of them being {{{n=2q}}} .
If you simplified the other one, your system is
{{{system(n=2q,n+5q=98)}}}
No matter what second equation you use, it is easy to substitute {{{2q}}} for {{{n}}} in the second equation, and just have one equation to solve for just the variable {{{q}}} .
I would use {{{n+5q=98}}} and substituting {{{2q}}} for {{{n}}} would get
{{{2q+5q=98}}} --> {{{7q=98}}} --> {{{q=98/7}}} --> {{{highlight(q=14)}}}
After that you find that the number of nickels is {{{2*14=28}}}
Using {{{5n+25q=490}}} you would substitute to get
{{{highlight(5*(2q)+25q=980)}}} .
Using {{{highlight(0.05n+0.25q=4.90)}}} you would substitute to get
{{{0.05*(2q)+0.25q=9.80}}} .
 
If you have not been taught about systems of linear equations, you may be expected to directly figure out one of the equations with just {{{q}}} highlighted above,
and then solve it,
without mentioning a "system of linear equations".
If you have been taught about systems of linear equations,
you may be expected to use fancy wording and format,
maybe mentioning a "system of linear equations" that you solve "by substitution".
 
VERIFICATION:
Getting that many of each coin from a willing adult,
asking for help in verifying your solution from a younger sibling who has learned to count money,
and afterwards sharing the profits
would be a satisfying and profitable learning experience for all involved.