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.
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 gte 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
Aug 09, 16 01:40 PM
Average age of Dipu and Apu is 22 years. Average age of Dipu and Tipu is 24 years. Age of Dipu is 21 years. What are the ages of Apu, and tipu ? Let
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.