Answer:
30 shirts
Step-by-step explanation:
Let x be the number of shirts a mercant bought initially.
He bought them for $120, so each shirt costed [tex]\frac{\$120}{x}[/tex]
The next day the price charged for each shirt was reduced by $1, so the new price of the shirt became
[tex]\dfrac{\$120}{x}-\$1[/tex]
The merchant calculated that, at the sale price, he could have bought 10 more shirts, so he could buy x + 10 shirts.
Number of shirts = x + 10
Price of each shirt [tex]=\dfrac{\$120}{x}-\$1[/tex]
Total cost = $120
Hence,
[tex](x+10)\left(\dfrac{120}{x}-1\right)=120\\ \\(x+10)(120-x)=120x\\ \\120x-x^2+1,200-10x=120x\\ \\-x^2-10x+1,200=0\\ \\x^2+10x-1,200=0\\ \\D=10^2-4\cdot (-1,200)=100+4,800=4,900\\ \\x_{1,2}=\dfrac{-10\pm \sqrt{4,900}}{2}=-40,\ 30.[/tex]
The number of shirts cannot be negative, so x = 30.
