Question 127486
Let N = the number of nickels and Q = the number of quarters.
Then:
{{{N+Q = 20}}} This is the total number of coins.
The value of N nickels is just {{{0.05N}}}
and the value of Q quarters is just {{{0.25Q}}} and the sum of these is $2.60
So now we have two equations:
{{{N+Q = 20}}} Rewrite this as: {{{N = 20-Q}}} and substitute in the equation below:
{{{0.05N+0.25Q = 2.60}}}
{{{0.05(20-Q)+0.25Q = 2.60}}} Simplify and combine like-terms.
{{{1-0.05Q+0.25Q = 2.60}}}
{{{1+0.2Q = 2.60}}} Subtract 1 from both sides.
{{{0.2Q = 1.6}}} Divide both sides by 0.2
{{{Q = 8}}}
Jim found 8 quarters. 
Check:
{{{0.05N+0.25Q = 2.60}}} Substitute Q = 8 and N = 20-8 = 12.
{{{0.05(12)+0.25(8) = 2.60}}}
{{{0.60+2.00 = 2.60}}}
{{{2.60 = 2.60}}}