Respuesta :
Answer:
The merchant buys 30 shirts originally.
Step-by-step explanation:
Let us assume that the merchant bought x numbers of shirts in $120.
So, the cost for each shirt is $[tex]\frac{120}{x}[/tex].
Now, if the cost for each shirt is reduced by 1$, then he would have bought 10 shirts more i.e. (x + 10) shirts in $120.
So, we can write the following equation as
[tex](\frac{120}{x} - 1)(x + 10) = 120[/tex]
⇒(120 - x)(x + 10) = 120x
⇒ 120x - 10x + 1200 - x² = 120x
⇒ x² +10x - 1200 = 0
⇒ x² + 40x - 30x - 1200 = 0
⇒(x + 40)(x - 30) = 0
⇒ x = - 40 or x = 30
But x can not be negative.
Hence, the merchant buys 30 shirts originally. (Answer)
