Question

Daca a+b=6000, b+c=5520, c+d=4000 si d+a =4480,sa se afle a ,b,c,d.

Answer 1

a + b             = 6 000

     b + c       = 5 520

            c + d = 4 000

a             +  d = 4 480

___________________ adun sumele date ( relatiile )

2 × a + 2 × b + 2 × c + 2 × d = 6 000 + 5 520 + 4 000 + 4 480

2 × ( a + b + c + d ) = 20 000 → dublul sumei numerelor

a + b + c + d = 20 000 : 2

a + b + c + d = 10 000 → suma numerelor

_______________________________

( a + b ) - ( b + c ) = 6 000 - 5 520

a + b - b - c = 480

a - c = 480 ⇒    a = c + 480

______________________

( b + c ) - ( c + d ) = 5 520 - 4 000

b + c - c - d =1 520

b - d = 1 520  ⇒  b = d + 1 520

___________________

( a + d ) - ( c + d ) = 4 480 - 4 000

a - d = 480 ⇒  a = d + 480

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Din relatiile : a = c + 480 = d + 480  ⇒    c = d

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a + b + c + d = 10 000

( d + 480 ) + ( d + 1 520 ) + d + d = 10 000

4 × d = 10 000 - ( 480 + 1 520 )

4 × d = 10 000 - 2 000

4 × d = 8 000

d = 8 000 : 4        ⇒     d = 2 000

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d + a = 4 480

2 000 + a = 4 480

a = 4 480 - 2 000       ⇒  a = 2 480

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c + d = 4 000            

c + 2 000 = 4 000

c = 4 000 - 2 000       ⇒   c = 2 000

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a + b = 6 000

2 480 + b = 6 000

b = 6 000 - 2 480      ⇒  b = 3 520