Please give the equation of this inequality

Question

Duchess, a dressmaker, ordered several meters of yellow cloth from a vendor, but the vendor only had 4 meters of yellow cloth in stock. The vendor bought the remaining lengths of yellow cloth from a wholesaler for PhP 1120. He then sold those lengths of yellow cloth to Duchess along with the original 4 meters of cloth for a total of PhP 1600. If the vendor's price per meter is at least PhP 10 more than the wholesaler's price per meter, what possible lengths of cloth did the vendor purchase from the wholesaler?

Answer 1

Hints:

Let $x$ be the length purchased from the wholesaler

Price per meter paid to wholesaler: $p_w = \dfrac{1120}{x}$

Price charged to customer per meter: $p_c =\dfrac{1600}{x+4}$

Stated inequality: $p_c \ge p_w+10$

Substitute and solve the quadratic inequality to get a range for $x$. For example $x=2$ and $x=200$ do not work, but $x=20$ does work