Question

There were 150 freshman and sophomores at the high school musical Reese and her friends attended. Freshman tickets were $2.00 each and sophomore tickets were $3.00 each. The receipts for freshman and sophomore tickets totaled $400. How many sophomores bought tickets?
Answer
75
100
25
50

Answer 1

Do this in your head:
If only freshmen attended, there would be only $300.
The extra $100 is generated by replacing 100 freshmen tickets with sophomore tickets.
So there are 100 sophomores and 50 freshmen.

Answer 2

We know that the total amount of people present is 150 (including sophmores and freshmen)
So, let # of sophmores attending = S
# of freshmen attending = F
So:1) S + F = 150
We also know that for each
Freshman, the ticket costs $2.00 each
And for Sophmores, they cost $3.00 per person
And we know that in total, $400 was spent.
So 2) 2F + 3S = 400

Rearranging 1) for S gives us:
S = 150-F
And substitution that into 2), gives us
2F + 3(150 - F) = 400
Isolating for F, we get:
F = 50, and using that number in 1) S = 100