Aaron needs to hire a waiter. waiter a is offering his services for an initial $20 in addition to $6.25 per hour. waitress b is offering her services for an initial $26 in addition to $5.25 per hour. when will the two waiters charge the same amount of money?

at 6 hours

establish equations for the 2 situations

let h be the hours worked by both

Waiter A : y = 6.25h + 20

Waiter B : y = 5.25h + 26

equate the right side of both equations

6.25h + 20 = 5.25h + 26 ( subtract 5.25h from both sides )

h + 20 = 26 ( subtract 20 from both sides )

h = 6

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)