Answer:
[tex]Quarters=78,\ Nickels=30[/tex]
Step-by-step explanation:
[tex]Let\ number\ of\ quarters=q\\\\Let\ number\ of\ nickels=n\\\\1\ quarter=$0.25\\\\1\ nickel=$0.05\\\\[/tex]
Total coins:
[tex]Given\ total\ coins=108\\\\quarters=q\\\\nickels=n\\\\q+n=108.............eq(1)[/tex]
Total Money:
[tex]Given\ total\ money=\$21\\\\Total\ money\ in\ quarters=number\ of\ quarters\times value\ of\ 1\ quarter=q\times 0.25\\\\Total\ money\ in\ quarters=0.25q\\\\Total\ money\ in\ nickels=number\ of\ nickels\times value\ of\ 1\ nickel=n\times 0.05\\\\Total\ money\ in\ quarters=0.05n\\\\0.25q+0.05n=21...............eq(2)[/tex]
[tex]eq(1)-4\times eq(2)\\\\q+n-4(0.25q+0.05n)=108-4\times 21\\\\q-q+n-0.2n=24\\\\0.8n=24\\\\n=\frac{24}{0.8}=30\\\\n=30\\\\Now\ from\ eq(1)\\\\q+n=108\\\\q=108-n=108-30\\\\q=78\\\\Quarters=78,\ Nickels=30[/tex]
