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Question 998795: The student council of XYZ School needed P225,000 for an annual trip. If five more members joined the group, each member would then save P500. How many students planned to make the trip?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = number of members.
let y = price per member.
c = the total cost.
formula to use is xy = c
since c = 225000, formula becomes:
xy = 225000
this formula states that the number of members times the price per member is equal to 225000.
if the number of members increases by 5, then the price per member decreases by 500.
the formula that represents that statement is:
(x+5) * (y-5) = 225000
you have 2 equations that need to be solved simultaneously.
they are:
xy = 225000 (first equation)
(x+5)*(y-500) = 225000 (second equation)
take that second formula and expand it to get:
xy - 500x + 5y - 2500 = 225000
since xy = 225000 from the first equation, you can replace xy with 225000 to get the second equation to become:
225000 - 500x + 5y - 2500 = 225000
the 225000 on the left side of the equal sign and the 225000 on the right side of the equal sign cancel out and you are left with:
-500x + 5y - 2500 = 0
from the first equation, you can also derive that y = 225000 / x.
you can replace y in the second equation with 225000 / x from the first equation to get the second equation to become:
-500x + 5 * (225000 / x) - 2500 = 0
multiply both sides of this equation by x to get:
-500x^2 + 5*225000 - 2500x = 0
divide both sides of this equation by -500 to get:
x^2 - 5*450 + 5x = 0
simplify to get:
x^2 - 2250 + 5x = 0
reorder the terms in descending order of degree to get:
x^2 + 5x - 2250 = 0
this is a quadratic equation that can be factored.
the factors are:
(x-45)*(x+50) = 0
solve for x to get:
x = 45 or x = -50
x has to be positive so x = 45.
when x = 45, y = 5000.
x * y = 45 * 5000 = 225000.
(x+5) * (y-500) = 50 * 4500 = 225000.
the requirements of the problem are satisfied.
the solution is that 45 members planned to make the trip.
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