The work of a student to solve a set of equations is shown: Equation 1: m = 8 + 2n Equation 2: 3m = 4 + 4n Step 1:−3(m) = −3(8 + 2n) [Equation 1 is multiplied by −3.] 3m = 4 + 4n [Equation 2] Step 2:−3m = −24 − 6n [Equation 1 in Step 1 is simplified.] 3m = 4 + 4n [Equation 2] Step 3: −3m + 3m = −24 − 6n + 4n [Equations in Step 2 are added.] Step 4:0 = −24 − 2n Step 5:n = −12 In which step did the student first make an error?

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.

i think the amount would be $140.62