Sharing money and equations

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