Question

Suma numerelor x si y este 20 si multimea { x ; y } este invers proportionala cu { 0,25 ; 0,(3) } . Determinati numerele .

Answer 1

Răspuns:

Explicație pas cu pas:

[x, y]  i.p.  [ 0,25;  0,(3)]

x/(1/0,25) = y/(1/0,(3) = k → coeficient de proportionalitate

x/(1/0,25) = k ⇒  0,25 x = k ⇒  x = k/0,25 =>  x = 4 k

 x : 1/0,25 = x × 0,25 = 25 x/100 = x/4 =>   x/4 = k = x = 4 k

y/(1/0,(3) = k  ⇒   y/3 = k  ⇒  y = 3 k

y : 1/0,(3) = 0,(3) y = 3 y/9 = y/3

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x + y = 20

4 k + 3 k = 20

7 k = 20     ⇒   k = 20/7

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x = 4 k ⇒  x = 4 × 20 /7  ⇒    x = 80/7

y = 3 k  ⇒  y = 3 × 20/7  ⇒     y = 60/7

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Verific:

x + y = 80/7 + 60 / 7 = 140/7 = 20

(80/7 )/ (1/0,25) = 80/7 × 1/4 = 20/7 (k)

(60/7)/[1/0,(3)] = (60/7) ×0,(3) = (60/7) × 1/3 = 20/7 (k)