Question 358951
1.{{{N+D+Q=30}}}
2.{{{5N+10D+25Q=450}}}
3.{{{N=3D}}}
Substituting eq. 3 into eq. 1,
{{{3D+D+Q=30}}}
4.{{{4D+Q=30}}}
Substituting eq. 3 into eq. 2,
{{{5(3D)+10D+25Q=450}}}
{{{25D+25Q=450}}}
5.{{{D+Q=18}}}
Subtract eq. 4 from eq. 5,
{{{4D+Q-D-Q=30-18}}}
{{{3D=12}}}
{{{highlight(D=4)}}}
Then from eq. 5,
{{{4+Q=18}}}
{{{highlight(Q=14)}}}
Then from eq. 3,
{{{N=3D}}}
{{{highlight(N=12)}}}
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12 nickels, 4 dimes, and 14 quarters.