Question 104837
n = number of nickels
d = number of dimes

value of one nickel is 5 cents, so the value of n nickels is 5n cents
value of one dime is 10 cents, so the value of d dimes is 10d cents

The number of dimes (d) is (=) 3 more (+3) than twice the number of nickels (2n), so


{{{d = 2n + 3}}} 


The value of the collection, that is the value of the dimes plus the value of the nickels is $1.80 or 180 cents, so


{{{5n + 10d = 180}}}


Substitute the expression for d from the first equation into the second equation:

{{{cartoon(5n + 10*red(d) = 180,5n + 10*red((2n+3))=180)}}}


Simplify and solve:

{{{5n + 10(2n+3)=180}}}
{{{5n+20n+30=180}}}
{{{25n=150}}}
{{{n=6}}}


{{{d=2(6)+3=15}}}


So there are {{{d+n=15+6=21}}} coins.


Check:

{{{10*15=150}}}
{{{5*6=30}}}
and {{{150+30=180}}}