Shelby bought 4 hamburgers and 2 orders of fries for $16.50. samuel bought 5 hamburgers and 3 orders of fries for $21.25 at the same time. how much did one hamburger cost?

Hamburgers costs $3.50 each.

x- Hamburgers

y- Fries

Shelby: 4x + 2y = $16.50

Samuel: 5x + 3y = $21.25

4x+2y=16.50

-4x       -4x

2y=-4x+16.50

Divide by 2

y = -2x+8.25

Then use substitution

5x + 3(-2x+8.25) = 21.25

5x -6x +24.75 = 21.25

x=3.50

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.