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?
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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.
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