Question

A collection of 108 coins containing only quarters and nickels is worth $21.

Which value could replace q on the chart?

Answer 1

Answer:

$Quarters=78,\ Nickels=30$

Step-by-step explanation:

$Let\ number\ of\ quarters=q\\\\Let\ number\ of\ nickels=n\\\\1\ quarter= 0.25\\\\1\ nickel= 0.05$

Total coins:

$Given\ total\ coins=108\\\\quarters=q\\\\nickels=n\\\\q+n=108.............eq(1)$

Total Money:

$Given\ total\ money=\ 21\\\\Total\ money\ in\ quarters=number\ of\ quarters\times value\ of\ 1\ quarter=q\times 0.25\\\\Total\ money\ in\ quarters=0.25q\\\\Total\ money\ in\ nickels=number\ of\ nickels\times value\ of\ 1\ nickel=n\times 0.05\\\\Total\ money\ in\ quarters=0.05n\\\\0.25q+0.05n=21...............eq(2)$

$eq(1)-4\times eq(2)\\\\q+n-4(0.25q+0.05n)=108-4\times 21\\\\q-q+n-0.2n=24\\\\0.8n=24\\\\n=\frac{24}{0.8}=30\\\\n=30\\\\Now\ from\ eq(1)\\\\q+n=108\\\\q=108-n=108-30\\\\q=78\\\\Quarters=78,\ Nickels=30$