Question 172826
I always start a problem like this by replacing the things 
I'm looking for with letters
Let {{{n}}} = number of nickels Joe has
Let {{{d}}} = number of dimes Joe has
Now I put in equation form the information I'm given
(1) {{{5n + 10d = 705}}}
Each term of this equation represents cents. In words:
(5 cents/nickel x # of nickels) + (10 cents/dime x # of dimes) = 705 cents
Or,if I wrote it the following way, each term represents dollars
{{{.05n + .1d = 7.05}}}, but it's the same equation
Also given:
(2) {{{5*(n + 8) + 10*(2d) = 1175}}}
Now I have 2 equations and 2 unknowns, so that's all I need to solve it
(2) needs some work
(2) {{{5*(n + 8) + 10*(2d) = 1175}}}
{{{5n + 40 + 20d = 1175}}}
{{{5n + 20d = 1135}}} 
Now subtract (1) from this
{{{10d = 1135 - 705}}}
{{{10d = 430}}}
{{{d = 43}}}
Joe has 43 dimes answer
Now substitute this in (1) to find {{{n}}}
(1) {{{5n + 10d = 705}}}
{{{5n + 10*43 = 705}}}
{{{5n = 705 - 430}}}
{{{5n = 275}}}
{{{n = 55}}}
Now I can check my answer:
(2) {{{5*(n + 8) + 10*(2d) = 1175}}}
{{{5*(55 + 8) + 10*(2*43) = 1175}}}
{{{5*63 + 10*86 = 1175}}}
{{{315 + 860 = 1175}}}
{{{1175 = 1175}}}
OK
And also
(1) {{{5n + 10d = 705}}}
{{{5*55 + 10*43 = 705}}}
{{{275 + 430 = 705}}}
{{{705 = 705}}}
OK