Question 175614
Number of nickels:  {{{n}}}


Number of dimes:  {{{d}}}


We know that {{{d = 7n}}} because Sally has seven times as many dimes as nickels.


Each of Sally's nickels is worth 5 cents, so the value, in cents, of all of Sally's nickels is {{{5n}}}.  Likewise, the value, in cents, of all of Sally's dimes is {{{10d}}}.


We know that the total value of Sally's coins is $3.00, but we can also say that the total value of her coins is 300 cents.  Now we can write:


{{{5n + 10d = 300}}}


But since we also know that {{{d = 7n}}}, we can substitute {{{7n}}} for {{{d}}}:


{{{5n + 10(7n) = 300}}}


Solving:


{{{5n + 70n = 300}}}


{{{75n = 300}}}


{{{n = 300/75 = 4}}}


Therefore Sally has 4 nickels.


Check:  If Sally has 4 nickels, she must have {{{7 * 4 = 28}}} dimes.  28 dimes are worth $2.80 and 4 nickels are worth $0.20 and $2.80 plus $0.20 is $3.00.  Answer checks.