Question

Știind ca 2x supra 3 = 3y supra 5 = 5z supra 4 si ca x+y+z=1, determina numerele x,y si z

Answer 1

Răspuns:

Explicație pas cu pas:

2x/3 = 3y/5 = 5z/4 = k  ->  coeficient de proportionalitate

2x/3 = k =>  x = 3k/2

3y/5 = k => y = 5k/3

5z/4 = k =>  z = 4k/5

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x + y + z = 1

3k/2 + 5k/3 + 4k/5 = 1   l × 30  ( c.m.m.m.c al numitorilor 2, 3 si 5 = 30 )

15 × 3 k + 10 × 5 k + 6 × 4 k = 30

45 k + 50 k + 24 k = 30

119 k = 30

k = 30/119

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x = 3 · 30/119 × ( 1/2)  =>    x =  45/119

y = 5 ·30/119 × ( 1/3)   ⇒    y = 50/119

z = 4 × 30/119 × ( 1/5) =>    z = 24/119

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x + y + z = 45/119 + 50/119 + 24/119 = 119/119 = 1