Tournament 5463

A reward of 1200 CZK is prepared for the 4 best champions in the chess tournament. It will be divided so that the second gets half of the first, the third half of the second's reward, and the fourth half of the third. How many CZK will each person receive? "

Correct answer:

a =  640
b =  320
c =  160
d =  80

Step-by-step explanation:


a+b+c+d=1200
b = a/2
c = b/2
d = c/2

a+b+c+d = 1200
a-2b = 0
b-2c = 0
c-2d = 0

Row 2 - Row 1 → Row 2
a+b+c+d = 1200
-3b-c-d = -1200
b-2c = 0
c-2d = 0

Row 3 - 1/-3 · Row 2 → Row 3
a+b+c+d = 1200
-3b-c-d = -1200
-2.3333c-0.3333d = -400
c-2d = 0

Row 4 - 1/-2.33333333 · Row 3 → Row 4
a+b+c+d = 1200
-3b-c-d = -1200
-2.3333c-0.3333d = -400
-2.1429d = -171.4286


d = -171.42857143/-2.14285714 = 80
c = -400+0.33333333333333d/-2.33333333 = -400+0.33333333 · 80/-2.33333333 = 160
b = -1200+c+d/-3 = -1200+160+80/-3 = 320
a = 1200-b-c-d = 1200-320-160-80 = 640

a = 640
b = 320
c = 160
d = 80

Our linear equations calculator calculates it.



Did you find an error or inaccuracy? Feel free to write us. Thank you!







Tips for related online calculators
Need help calculating sum, simplifying, or multiplying fractions? Try our fraction calculator.
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?

You need to know the following knowledge to solve this word math problem:

Related math problems and questions: