let x = the amount of money he gets his commission on per day.
he makes 30 dollars plus .05 * x every day at future store.
he makes 40 dollars plus .04 * x every day at buy the best.
in order to make future store a better place to work, he needs to make more there than he would at buy the best.
that leads to the following equation:
30 + .05 * x > 40 + .04 * x
subtract 30 from both sides of this inequality to get:
.05 * x > 40 + .04 * x - 30
subtract .04 * x from both sides of this inequality to get:
.05 * x - .04 * x > 40 - 30
combine like terms to get:
.01 * x > 10
divide both sides of this inequality by .01 to get:
x > 10/.01
solve for x to get:
x > 1000
he needs to sell more than 1000 dollars of merchandise in order to make future store a better place to work than buy the best, assuming money is the determining factor.
he will break even when he sells 1000 dollars worth of merchandise.
he will do better when he sells more than 1000 dollars worth of merchandise.
when x = 1000,
money at future store = 30 + .05 * x = 30 + 50 = 80
money at buy the best = 40 + .04 * x = 40 + 40 = 80
when x = 1200,
money at future store = 30 + .05 * x = 30 + 60 = 90
money at buy the best = 40 + .04 * x = 40 + 48 = 88
the following table shows <, =, > values:
future store buy the best
x 30 + .05 * x 40 + .04 * x
800 70 72
1000 80 80
1200 90 88
the break even is when x = 1000
after that, future store money is greater than buy the best money.