James went to the theatre to watch a concert with his family. The theatre had 1750 seats. There were 60% fewer $50-seats than $30-seats. 50% of the $30-seats and some $50-seats were sold. A total of $20 000 was collected. How many seats were unsold?

To solve this problem, we need to break it down into several steps:

Step 1: Determine the number of $30 and$50 seats.

The problem states that there were 60% fewer $50 seats than$30 seats. Let's denote the number of $30 seats as x. Therefore, the number of$50 seats is 0.4x (since it's 60% fewer).

The total number of seats in the theatre is 1750, so we can set up the following equation: x + 0.4x = 1750. Solving this equation gives us x = 1250. This means there were 1250 $30 seats and 0.4*1250 = 500$50 seats.

Step 2: Determine the number of sold seats and the total revenue.

The problem states that 50% of the $30 seats were sold, which is 0.5*1250 = 625 seats.

We also know that the total revenue was $20,000. The revenue from the$30 seats is 625*$30 =$18,750. Therefore, the revenue from the $50 seats is$20,000 - $18,750 =$1,250.

Since each $50 seat costs$50, the number of $50 seats sold is$1,250/$50 = 25 seats.

Step 3: Determine the number of unsold seats.

The total number of sold seats is 625 (from the $30 seats) + 25 (from the$50 seats) = 650 seats.

Therefore, the number of unsold seats is the total number of seats in the theatre minus the number of sold seats, which is 1750 - 650 = 1100 seats.

So, there were 1100 unsold seats.