## SAT Math Tutorial

*SAT algebra *

#### Sample Problem

A company’s manager estimated that the cost C, in dollars, of producing n items is C = 7n + 350. The company sells each item for $12. The company makes a profit when total income from selling a quantity of items is greater than the total cost of producing that quantity of items. Which of the following inequalities gives all possible values of n for which the manager estimates that the company will make a profit?

#### Solution

The cost of making n products is given by:

C = 7n + 350

Since the company sells each product for $12, the company’s income for n products is:

I = 12n

The company makes a profit when the total income is greater than the cost, so we need:

I > C

12n > 7n + 350

12n – 7n > 350

5n > 350

n > 70

So the company makes a profit if it sells more than 70 items (n > 70).

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