1. ## Verbal Problem

A street corner vendor buys roses for $9.12 per dozen and sells them at$1 each. His costs of operation are $34 per day. If x represents the number of roses he sells in a day, express his profit for the day in terms of x. Can some one help me with this? thx 2. Profit = Revenue - Cost If he buys them for$9.12 per dozen roses, that means that his cost from the roses is $\displaystyle \frac{9.12x}{12} = \frac{19x}{25}$. He also has a fixed cost of $34 a day. Therefore if we let C be the cost,$\displaystyle C = \frac{19x}{25} + 34$. He is earning$1 for every rose. So his revenue (R) is $\displaystyle R = x$.

Therefore, if we let P represent the profit per day, we have

$\displaystyle P = R-C$

$\displaystyle P = x - \left(\frac{19x}{25} + 34\right)$

$\displaystyle P = \frac{25x}{25} - \frac{19x}{25} - 34$

$\displaystyle P = \frac{6x}{25} - 34$.