Question

A beautician charges $\$15$ for a manicure. Her operating expense is $\$35$ per day (average). She calculates her profit by subtracting her operating costs from the money she earns from the manicure she gives. In a given day, the beautician expects to make a profit of at least $\$85$. If the beautician gives m manicure in a day. Which inequality best models this situation?

• A. $15m-35\ge 85$
• B. $15(m-35)\ge 85$
• C. $15m+35\ge 85$
• D. $15(m+35)\ge 85$

Answer 1

The correct option is A $15m-35\ge 85$

The beautician wants to make a profit of at least $\$85$. Since profit is total revenue minus the operating cost, where revenue is the price per unit times the number of units sold, we can model this situation with an inequality
Total revenue - expenses $\ge$ 85
The beautician total revenue is 15m, we know the expenses for the day is $\$35$ 35 lets model the whole situation with the inequality $15m-35\ge 85$