Kevin and randy muise have a jar containing 87 coins, all of which are either quarters or nickels. the total value of the coins in the jar is $12.55. how many of each type of coin do they have?

Let x be the amount of nickels and y be the amount of quarters in a jar. Totally there are 87 coins, then x+y=87.

Since nickel is 5 cent coin and quarter is 25 cent coin, then 5x+25y=1255 ($12.55=1255 cents). Solve this system:x=87-y and 5(87-y)+25y=1255.
435-5y+25y=1255,
25y-5y=1255-435,

20y=820,
y=820÷20,
y=41,
x=87-41=46.
46 nickels and 41 quarters.