Question

For a Valentine's Day dance, tickets for couples cost $12 and tickets for individuals cost $8. Suppose 250 students attended the dance, and $1580 was collected from ticket sales. How many of each type of ticket was sold?

PLEASE DO THIS IN ELIMINATION OR GRAPHING METHOD (NOT substitution method, as I already did it like this)
​

Answer 1

Explanation:

Let's imagine if all the tickets were for individuals

The cost would be 250 x $8 = $2000
That is $420 higher than the actual cost.

The difference between a ticket for couples and a ticket for individuals is $4

Then, we can conclude that there are 420 : 4 = 105 couple tickets that were sold.

And, 40 individual tickets that were sold

The reason why we have 420:4 is because at the start, we assume every ticket was individuals. On the process, we replace one individual ticket by a couple ticket, keep replacing until the gap is exactly 420.

Hope this helps :)

Answer 2

Answer: 105 couple tickets and 40 individual tickets

For this I will use the "Graphing Method"

First, we need to set up two equations.

-> Let x be the number of couple tickets.

-> Let y be the number of individual tickets.

-> It is "2x" because a couple means two.

$12x + $8y = $1,580

2x + y = 250

Next, we will graph this.

-> The point at which the two lines intersect is our solution.

-> See attached.

-> x = 105, so 105 couple tickets

-> y = 40, so 40 individual tickets

Have a nice day!

I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.

- Heather