Question 314797
N-number of nickels
D-number of dimes
Q-number of quarters
.
.
1.{{{N+D+Q=30}}}
2.{{{5N+10D+25Q=550}}}
3.{{{D=2N}}}
Substitute eq. 3 into both 1 and 2.
{{{N+2N+Q=30}}}
4.{{{3N+Q=30}}}
.
.
{{{5N+10(2N)+25Q=550}}}
{{{5N+20N+25Q=550}}}
{{{25N+25Q=550}}}
5.{{{N+Q=22}}}
Multiply eq. 4 by (-1) and add to eq. 5.
{{{-3N-Q+N+Q=-30+22}}}
{{{-2N=-8}}}
{{{highlight(N=4)}}}
Then from eq. 5,
{{{4+Q=22}}}
{{{highlight(Q=18)}}}
and from eq. 3,
{{{D=2N}}}
{{{highlight( D=8)}}}