PROBLEM
The student council of Sta. Lucia High School needed Php. 2,250 for an annual trip. If 5 more members joined the group, each member would then save Php 5. How many students planned to make the trip?
x = number of students
p = price of ticket
x p = 2250
(x+5)(p-5) = 2250
p = 2250/x
xp + 5 p - 5 x - 25 = 2250
xp + 5 p - 5 x - 2275 = 0
2250 + 11250/x - 5 x - 2275 = 0
11250 - 5 x^2 - 25 x = 0
x^2 + 5 x - 2250 = 0
(x+50) (x-45) = 0
x = 45
To find the number of students who planned to make the trip, we can set up an equation based on the given information.
Let's assume the original number of students in the group is x.
The total amount needed for the trip is Php 2,250.
If 5 more members join the group, the new total number of students in the group would be x + 5.
The new amount saved by each member would be Php 5.
We can set up the equation:
(x + 5) * 5 = 2250
Now, let's solve for x.
First, distribute the 5:
5x + 25 = 2250
Subtract 25 from both sides of the equation:
5x = 2225
Divide both sides of the equation by 5:
x = 445
Therefore, the original number of students who planned to make the trip was 445.
But, we assumed the original number of students. To be more accurate, we should subtract the 5 students who joined later:
x = 445 - 5 = 440
So, there were 440 students who initially planned to make the trip.
To solve this problem, we need to set up an equation based on the given information.
Let's assume the original number of students planning to make the trip is x.
According to the problem, the total amount needed is Php 2,250, and each student would save Php 5 more if 5 more members joined.
So, the equation can be set up as follows:
(x + 5) * (x + 5 + 5) = 2250
Let's solve this equation step by step:
1. Simplify the expression inside the parentheses:
(x + 5) * (x + 10) = 2250
2. Expand the equation by multiplying:
x^2 + 10x + 5x + 50 = 2250
3. Combine like terms:
x^2 + 15x + 50 = 2250
4. Move 2250 to the other side of the equation by subtracting it:
x^2 + 15x + 50 - 2250 = 0
5. Simplify the equation:
x^2 + 15x - 2200 = 0
Now, we have a quadratic equation. We can solve it by factoring or using the quadratic formula. Since factoring is not apparent, we will use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = 15, and c = -2200.
Plugging these values into the quadratic formula:
x = (-15 ± √(15^2 - 4*1*(-2200))) / (2*1)
Simplifying:
x = (-15 ± √(225 + 8800)) / 2
x = (-15 ± √9025) / 2
x = (-15 ± 95) / 2
Using the positive square root:
x = (-15 + 95) / 2
x = 80 / 2
x = 40
Therefore, the original number of students planning to make the trip is 40.