SOLUTION: tutors help me with this plz... i tried to solve it but i didn't get the right answer..pls help. 9. The student council of Sta Lucia High School needed $2250 for an annual trip.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: tutors help me with this plz... i tried to solve it but i didn't get the right answer..pls help. 9. The student council of Sta Lucia High School needed $2250 for an annual trip.      Log On


   

Question 55448: tutors help me with this plz... i tried to solve it but i didn't get the right answer..pls help.
9. The student council of Sta Lucia High School needed $2250 for an annual trip. If five more members joined the group, each member would then save $5. How many students planned to make the trip?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
. The student council of Sta Lucia High School needed $2250 for an annual trip. If five more members joined the group, each member would then save $5. How many students planned to make the trip?
:
We have two values for the number of students:
:
Let x = original number of students
Then (x+5) = number of students if 5 more join
:
The amt each student must pay originally:
2250/x
:
The amt each student must pay, if 5 more join:
2250/(x+5)
:
"If five more members joined the group, each member would then save $5."
What this says essentially:
original amt - $5 equals amt if 5 more join
%282250%2Fx%29+-+5+=+%282250%2F%28x%2B5%29%29
:
Mult eq by x(x+5) to get rid of the denominators, we then have:
2250(x+5) - 5(x(x+5) = 2250x
:
2250x + 11250 - 5x^2 + 25x = 2250x
:
-5x^2 + 2250x - 2250x - 25x + 11250
:
-5x^2 - 25x + 11250
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Simplify divide equation by -5 and you have:
x^2 + 5x - 2250 = 0; a manageable equation
Factors to:
(x + 50) (x - 45) = 0
:
We want the positive solution only:
x = +45 students originally
:
Check: 2250/45 = $50 ea and 2250/50 = $45 ea
:
Not that hard, right?