A credit card company offers a cash back program on transactions. For every transaction over $100 the customer gets $3 back. For every transaction $100 or less, the customer gets $1 back. The customer made 24 transactions in all and the total number of dollars given back was $32. Write and solve a system of equations to
find the number of transactions of each type.

step-by-step explanation:

so then what are you asking?

step-by-step explanation:

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.