## SAT Math Tutorial

#### Intro

This is an SAT math question looking at cost, income and profit.

#### Sample Problem

Question source

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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