Question

5 tiffany makes scarves and sells them at a neighborhood clothing store. the owner charges her $25 a day for the space she uses. she sells each scarf for $30. each scarf costs her $14 to make. how many scarves must tiffany sell per day to make a profit of at least $100 per day? write and solve an inequality. show your work.

Explanation:

Step1: Define variable for scarves

Let $x$ = number of scarves sold daily.

Step2: Calculate profit per scarf

Profit per scarf = Selling price - Cost to make
$\$30 - \$14 = \$16$

Step3: Set up profit inequality

Total profit = (Profit per scarf $\times x$) - Daily space fee. This must be at least $\$100$.
$16x - 25 \geq 100$

Step4: Isolate the variable term

Add 25 to both sides.
$16x \geq 100 + 25$
$16x \geq 125$

Step5: Solve for x

Divide both sides by 16.
$x \geq \frac{125}{16}$
$x \geq 7.8125$

Step6: Round up to whole number

Scarves are whole units, so round up.
$x \geq 8$

Answer:

Tiffany must sell at least 8 scarves per day.