Kevin and Randy Muise have a jar containing 51 ​coins, all of which are either quarters or nickels. The total value of the coins in the jar is ​$5.75. How many of each type of coin do they​ have?

Let x = the number of quarters

Let y = the number of nickels

X + y = 62     x = 62 - y

.25x + .05y = 12.50              Multiply both sides of the equation by 100 to get rid of the decimal points.

25x + 5y = 1250

25(62-y) + 5y = 1250

1550 - 25y + 5y = 1250

-20y = -300

y = 15 nickels

x = 62 - y = 62 - 15

x = 47 quarters

answer: the common difference is -0.10

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.