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.



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

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