Question

a) Daca x/3=y/4 si 3x +4y=75, determinati x si y

b)Daca x/5=y/7 si x+y=24 , determinati x si y

c)Daca x/4=y/7, atunci 9x-2y/x+3y=

d)Daca x/2=y/9 atunci 10x-2y/5x+y=

Answer 1

Răspuns:

Explicație pas cu pas:

a)   x/3 = y/4 = k ⇒   x = 3 k   si   y = 4 k

3 x + 4 y = 75

3 × 3 k + 4 × 4 k = 75

9 k + 16 k = 75

25 k = 75

k = 75 : 25     ⇒   k = 3

x = 3 × 3         ⇒   x = 9

y = 4 × 3         ⇒   y = 12

Verific:    3 × 9 + 4 × 12 = 27 + 48 = 75

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b)

x/5 = y/7 = k   ⇒  x = 5 k   si   y = 7 k

x + y = 24

5 k + 7 k = 24

12 k = 24

k = 24 : 12    ⇒      k = 2

x = 5 × 2       ⇒      x = 10

y = 7 × 2       ⇒      y = 14

Verific:    x + y =  10 + 14 = 24

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c)

x/4 = y/7 = k → coeficient de proportionalitate

⇒  x = 4 k    si  y = 7 k

( 9 x - 2 y ) / ( x + 3y) = 22/25

= ( 9 × 4 k - 2 × 7 k ) / ( 4 k + 3 × 7 k ) =

= ( 36 k - 14 k ) / ( 4 k + 21 k ) =

= 22 k / 25 k =

= 22/25

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d)  

x/2 = y/9 = k ⇔   x = 2 k   si   y = 9 k

( 10 x - 2y) / ( 5x + y) = 2/19

= ( 10 × 2k - 2 × 9 k ) / ( 5 × 2 k + 9 k ) =

= ( 20 k - 18 k ) / ( 10 k + 9 k ) =

= 2 k / 19 k =

= 2/19