by Rea Alimeri
(Albania)
A certain value of money will be distributed among 24 students. If 6 students don't come each child will receive 300 dollars more money. Find the amount of money.
Solution
Let x be the amount that will be distributed.
Let y be the amount each student gets.
The money will be distributed among 24 students.
Since the amount is x, we can do x/24.
x/24 should equal to y
x/24 = y
If 6 students don't come, the money will be distributed between
24 - 6 students or 18 students.
Now, what is the money that will be distributed now between 18 students?
Since the amount is still x, we get x/18
Since each child will get 300 dollars more, what each child will get is equal to y + 300
x/18 = y + 300
We just have to solve two equations
x/24 = y equation 1
x/18 = y + 300 equation 2
Multiply equation 1 by 24
We get x = 24y
Replace the value of x into equation 2
24y/18 = y + 300
4y/3 = y + 300
4y/3 - y = 300
4y/3 - 3y/3 = 300
(4y - 3y) / 3 = 300
y / 3 = 300
Multiply both sides by 3
3y/3 = 3 × 300
y = 900
Each student will get 900 dollars.
x/24 = 900
Multiply both sides by 24
24x/24 = 24 × 900
x = 21600
Let us verify the condition of the problem
21600 / 18 = 1200
1200 - 900 = 300
So indeed, each student will get 300 dollars more