Question 1172083
problem number 1:


let x = the total amount sold.
let y = the commission.
you have a split function.
y = 0 when x <= 10,000
y = .035 * (x - 10,000) when x is greater than 10,000.
if he makes 1400 commission, you can assume he sold more than 10,000 worth.
your equation is therefore:
y = .035 * (x - 10,000)
simplify to get:
y = .035 * x - .035 * 10,000
simplify further to get:
y = .035 * x - 350
when y = 1400, the equation becomes:
1400 = .035 * x - 350
add 350 to both sides of the equation to get:
1750 = .035 8 x
solve for x to get:
x = 1750 / .035 = 50,000
if he sells 50,000 worth in sales, he will make 1400 in commission.
it works like this.
he makes 0 commission on sales totaling 10,000.
he makes 3.5% commission on all sales over 10,000.
this becomes 50,000 - 10,000 = 40,000 worth of sales over 10,000.
that gets you .035 * 40,000 = 1400.
solution is confirmed to be good.
he must sell 50,000 in a month in order to earn a commission of 1400 for that month.