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
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 xy=2250. The second sentence means (x+5)(y5)=2250. From the first equation one gets y=2250x.
Substituting this value of y in the second equation gives (x+5)(2250x5)=2250. Multiplying the factors on the left yields the equation 2250+22505x5x25=2250. Subtracting 2250 from both sides yields 22505x5x25=0. Multiplying both sides by x5 yields 2250x25x=0.

By the quadratic equation, one gets x=5(+)254(1)(2250)2. So, x = 5(+)90252 or x = 5(+)952. Since x can't be negative, it means the answer is x = 5952 or 45.