Question

Tickets for a certain show cost ​$17​, ​$21​, ​or, for VIP​ seats, ​$40. If ten times as many ​$17 tickets were sold as VIP​ tickets, and the number of ​$17 tickets sold was 57 more than the sum of the number of ​$21 tickets and VIP​ tickets, sales of all three kinds of tickets would total ​$51 comma 471. How many of each kind of ticket would have been​ sold?

Answer 1

Answer:

Tickets sold:

VIP $=126$

$17 tickets $=1,260$

$21 tickets $=9\cdot 126+57=1,191$

Step-by-step explanation:

Let x be the number of VIP tickets.  

If ten times as many ​$17 tickets were sold as VIP​ tickets, then the number of $17 tickets is $10x.$

If the number of ​$17 tickets sold was 57 more than the sum of the number of ​$21 tickets and VIP​ tickets, then $10x+57=x+y$ and the number y of $21 tickets is $9x+57.$

Amounts earned:

VIP tickets $=\ 40x$

$17 tickets $=\ 17\cdot 10x=\ 170x$

$21 tickets $=\ 21\cdot (9x+57)=\ (189x+1,197)$

Total $=\ (40x+170x+189x+1,197)=\ (399x+1,197)$

The sales of all three kinds of tickets would total ​$51,471, so

$399x+1,197=51,471\\ \\399x=51,471-1,197\\ \\399x=50,274\\ \\x=126$

Tickets sold:

VIP $=126$

$17 tickets $=1,260$

$21 tickets $=9\cdot 126+57=1,191$