Answer:
The number of quarters is 47 and the number of nickels is 49.
Explanation:
Let the number of quarters be x and the number of nickels be y.
Kevin and Randy Muise have a jar containing 96 coins, all of which are either quarters or nickels.
[tex]x+y=96[/tex] .... (1)
1 quarters = 0.25 dollars
1 nickels = 0.05 dollars
The total value of the coins in the jar is $14.20.
[tex]0.25x+0.05y=14.20[/tex] .... (2)
From (1) and (2), we get
[tex]0.25(96-y)+0.05y=14.20[/tex]
[tex]2400-25y+5y=1420[/tex]
[tex]-20y=-980[/tex]
[tex]y=49[/tex]
Put this value in equation (1).
[tex]x+49=96[/tex]
[tex]x=96-49[/tex]
[tex]x=47[/tex]
The value of x is 47 and the value of y is 49. Therefore the number of quarters is 47 and the number of nickels is 49.
