For the opening night at the Opera House, a total of 1000 tickets were sold. Front orchestra seats cost $90 apiece, rear orchestra seats cost $70 apiece, and front balcony seats cost $60 apiece. The combined number of tickets sold for the front orchestra and rear orchestra exceeded twice the number of front balcony tickets sold by 400. The total receipts for the performance were $72,000. Determine how many tickets of each type were sold.

Step-by-step explanation:

GIVEN: For the opening night at the Opera House, a total of tickets were sold. Front orchestra seats cost apiece, rear orchestra seats cost  apiece, and front balcony seats cost apiece. The combined number of tickets sold for the front orchestra and rear orchestra exceeded twice the number of front balcony tickets sold by . The total receipts for the performance were .

TO FIND: how many tickets of each type were sold.

SOLUTION:

Let the number of Front orchestra seats sold

Let the number of rear orchestra seats sold

Let the number of Front balcony seats sold

total number of tickets sold  

Now,

The combined number of tickets sold for the front orchestra and rear orchestra exceeded twice the number of front balcony tickets sold by .

solving both equations we get,

total revenue from Front balcony seats

total revenue from front and rear orchestra

total revenue from front and rear orchestra

Solving both equations we get,

Hence total front orchestra, rear orchestra and front balcony tickets sold are

yes the total will be same because in both of them the expression.is rearranged but their sign remains the same hence it hss just been shuffled