The band at Brown High School sells tickets for catered dinners to raise money for field trips. Spaghetti dinner
tickets cost $7.25, and barbecue dinner tickets cost $8.75. The band sold twice as many spaghetti dinners as
barbecue dinners and raised $2,790. Which of the following sets of equations can be used to determine the number
of spaghetti dinner tickets, x, and the number of barbecue dinner tickets, y, sold?
x = 2y
7.25x + 8.75y = 2,790
2x = y
7.25x + 8.75y = 2,790
© x = 2y
8.75x + 7.25y = 2,790
© 2x = y
8.75x + 7.25y = 2,790

You know that 1 spaghetti dinner ticket costs $7.25; so the total amount of money earned selling these tickects can be represented with this expression:

[tex]7.25x[/tex]

Since 1 barbecue dinner ticket costs $8.75; the total amount of money earned selling them can be represented with this expression:

[tex]8.75y[/tex]

Knowing that the total amount of money the band raised was $2,790, we can write the following equation to represent this situation:

[tex]7.25x+8.75y=2,790[/tex]

The band sold twice as many spaghetti dinners as barbecue dinners, which means that the amount of spaghetti dinners sold was two times the amount of barbecue dinners sold.

This can be represented with this equation:

[tex]x=2y[/tex]

Therefore, the set of equations that can be used to find "x" and "y", is:

[tex]\left \{ {{x=2y} \atop {7.25x+8.75y=2,790}} \right.[/tex]