115k views
5 votes
A merchant bought some shirts for $120. The next day the price charged for each shirt was reduced by $1. The merchant calculated that, at the sale price, he could have bought 10 more shirts for $120. How many shirts did he buy originally?

1 Answer

4 votes

Answer:

The merchant buys 30 shirts originally.

Explanation:

Let us assume that the merchant bought x numbers of shirts in $120.

So, the cost for each shirt is $
(120)/(x).

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


((120)/(x) - 1)(x + 10) = 120

⇒(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)

User Jinu
by
8.8k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.