Question 1144362
formula for acme is y = 40 * x + 100
formula for hank is y = 65 * x


hank cost less than acme when 65 * x < 40 * x + 100
subtract 40 * x from both sides of this equation to get:
65 * x - 40 * x < 100
combine like terms to get:
25 * x < 100
solve for x to get:
x < 100 / 25 which becomes x < 4.


hank will be cheaper than acme when the number of hours required to finish the job is less than 4 hours.


the two equations for hank and acme can be graphed.
the graph shows where the break even point and when hank is cheaper and when acme is cheaper.


the graph is shown below.


<img src = "http://theo.x10hosting.com/2019/082901.jpg" alt="$$$" >


the red line is hank.
the blue line is acme.


you can see that the break even point is 4 hours.
when the number of hours is less than 4, hank is cheaper (red line is below the blue line),
when the number of hours is greater than 4, acme is cheaper (blue line is below the red line).