Question 1138560
A bag contains {{{39}}} coins, all nickels and quarters. The total value of the coins in the bag is ${{{6.35}}}. How many of the coins are nickels? 

let nickels be {{{n}}} and quarters {{{q}}}

given:
{{{n+q=39}}}....solve for {{{n}}}

{{{n=39-q}}}.........eq.1

the total value of the coins in the bag is ${{{6.35}}}


{{{1n}}}=${{{0.05}}}
{{{1q}}}=${{{0.25}}}

then, we have

{{{0.05n+0.25q=6.35}}}.....eq.2......substitute {{{n}}} from eq.1

{{{0.05(39-q)+0.25q=6.35}}}

{{{1.95-0.05q+0.25q=6.35}}}

{{{-0.05q+0.25q=6.35-1.95}}}

{{{0.20q=4.40}}}

{{{q=4.40/0.20}}}

{{{q=44/2}}}

{{{q=22}}}

go to {{{n=39-q}}}.........eq.1 substitute {{{q}}}

{{{n=39-22}}}

{{{n=17}}}

there are {{{17}}} nickels