Question 992291
equation for plan A is ca = 38 + .20 * x
equation for plan B is cb = 57.04 + .12 * x


question is for how many miles driven would you save money with plan B.


you will save money with plan B when the cost of plan B is less than the cost of plan A.


this means that cb < ca


replace cb with it's equation and replace ca with its equation to get:


57.04 + .12 * x < 38 + .20 * x


subtract 38 from both sides of this equation and subtract .12 * x from both sides of this equation to get:


57.04 - 38 < .20 * x - .12 * x


combine like terms to get:


19.04 < .08 * x


divide both sides of this equation by .08 to get:


19.04 / .08 < x


238 < x


solve for x to get x > 238 miles.


when x = 238 miles, plan A costs 85.6 and plan B costs 85.6.
plan B costs the same as plan A.
this is the break even point.


when x = 239 which is greater than 238, plan A costs 85.8 and plan B costs 85.72.
plan B is now cheaper than plan A and will remain cheaper as long as the number of miles driven is greater than 238.