Answer: 1200 people came to the party.
Step-by-step explanation:
Let x represent the number of singles tickets that were sold.
Let y represent the number of couples tickets that were sold.
A total of 850 tickets were sold for the party. It means that
x + y = 850
If tickets cost $3 for couples and $2 for singles and the total sales generated was $2050, it means that
2x + 3y = 2050- - - - - - - - - -1
Substituting x = 850 - y into equation 1, it becomes
2(850 - y) + 3y = 2050
1700 - 2y + 3y = 2050
- 2y + 3y = 2050 - 1700
y = 350
x = 850 - y = 850 - 350
x = 500
Since a couples ticket is for 2 people, it means that the number people that bought the couples tickets is
2 × 350 = 700
Therefore, the total number of people that came to the party is
500 + 700 = 1200
