Question

a company can model the profit it makes on selling an item at price x by using the expression 2000x - 10,500. a second item sold at the same price brings in a profit og 1850x - 11,600. write and simplify an expression that reflects the total profit from the sale of both items

Answer 1

Profits are simply the difference between the selling price and the cost price of an item.

The expression that represents the total profit is 3850x - 22100

The profit (p1) on the first item is given as:

$p_1 = 2000x - 10500$

The profit (p2) on the second item is given as:

$p_2 = 1850x - 11600$

So, the total profit (p) on the sales of both items is:

$p = p_1 + p_2$

Substitute known values

$p = 2000x - 10500 + 1850x - 11600$

Collect like terms

$p = 2000x + 1850x- 10500 - 11600$

$p = 3850x-22100$

Hence, the expression that represents the total profit is 3850x - 22100

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