The student council of sta.Lucia high school needed 2,250 pesos for an annual trip.If five more members joined the group,each member would then save 5pesos. How many students planned to make a trip?

1 Answer
Prof_S
Jan 9, 2016

The answer is 45.

Explanation:

Let x be the number of students and y be the cost per student. The first sentence means #x*y = 2250#. The second sentence means #(x+5)(y-5)=2250#. From the first equation one gets #y = 2250/x#.
Substituting this value of y in the second equation gives #(x+5)*(2250/x - 5) = 2250#. Multiplying the factors on the left yields the equation #2250 + (2250*5)/x - 5x -25 = 2250#. Subtracting 2250 from both sides yields #(2250*5)/x - 5x -25 = 0#. Multiplying both sides by #x/5# yields #2250 - x^2 - 5x = 0#.

By the quadratic equation, one gets #x = (5 (+/-) sqrt(25 - 4(-1)(2250)))/-2#. So, x = # (5 (+/-) sqrt(9025))/-2# or x = #(5 (+/-) 95)/-2#. Since x can't be negative, it means the answer is x = #(5 - 95)/-2# or 45.

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