Question

The Northwest High School senior class decided to host a raffle to raise money for their senior trip. They charged $2 for each student raffle ticket and $5 for each adult raffle ticket and they raised $2,686 from ticket sales. If adults bought 3 times as many tickets as students, how many tickets did the senior class sell?

2x + 5y = 2,686
y = 3x

Northwest High School’s senior class sold ___ raffle tickets.

Answer 1

the senior class sold 632 raffle tickets.

Explanation:

got it right on edge 2020

Answer 2

Let
`x` be the tickets that the adults bought, and
`y` be the tickets that children bought.
From the problem we have the system of linear equations:

`\left \{ {{2x+5y=2686} \atop {y=3x}} \right.`

The first thing we are going to do to solve our system, is replacing equation (2) in equation (1), and then, solve for
`x`

`2x+5y=2686`

`2x+5(3x)=2686`

`2x+15x=2686`

`17x=2686`

`x= (2686)/(17)`

`x=158`

Now that we have the number of tickets that the adults bought, lets replace that value in equation (2):

`y=3x`

`y=3(158)`

`y=474`

Last but not least, to find the total number of tickets, we are going to add
`x` and
`y`:

`158+474=632`

We can conclude that Northwest High School's senior class sold 632 raffle tickets.