SOLUTION: a school planning a field trip to a theatre to see a play whose tickets normally sell for $28. the business manager of theater will discount the ticket price by $0.15 per students

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Question 1161856: a school planning a field trip to a theatre to see a play whose tickets normally sell for $28. the business manager of theater will discount the ticket price by $0.15 per students attending. the chartered bus will cost $350 regardless of the number of students attending the play and will be split equally among those students attending the play. who many students must attend to keep the total cost per student between $10 and $20?

Answer by ankor@dixie-net.com(22740) (Show Source):
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a school planning a field trip to a theatre to see a play whose tickets normally sell for $28.
the business manager of theater will discount the ticket price by $0.15 per students attending.
the chartered bus will cost $350 regardless of the number of students attending the play and will be split equally among those students attending the play.
how many students must attend to keep the total cost per student between $10 and $20?
:
let x = number of students, strive for $15 per student
(28 - .15x) + = 15
-.15x + = 15 - 28
-.15x + = -13
multiply thru by -x, get rid of the denominator and the neg
.15x^2 - 350 = 13x
A quadratic equation
.15x^2 - 13x - 350 = 0
using the quadratic formula, I got a positive x = 108.2264
Obviously we have to have integer kids let's see how 109 kids check out
.15(109^2) - 13(109) - 350 = 15.15
With 109 kids, each will pay about $15 to attend the play
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See how that checks out in the original equation
28 - .15(109) + 350/109 = 14.86 ~ 15