Question

3)Dacă:
b)7x/8y-7x=7/9,aflați x/y
c)2x+3y/2x+4y=13/16,aflați x/y
d)5x+3y/2x=3y=58/34,aflați y/x
e)7x+2y/4x+7y=11/18,aflati x/y
f)3x+y/4x+3y=9/17,aflați 4x+y/x+2y

Answer 1

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(b)

7x/(8y - 7x) = 7/9

7·(8y - 7x) = 7x·9    |:7

8y - 7x = 9x

8y = 9x + 7x

8y = 16x   |:8

y = 2x

2x = y

x/y = 1/2

c)

(2x + 3y)/(2x + 4y) = 13/16

13(2x + 3y) = 16(2x + 4y)

26x + 52y = 32x + 48y

52y - 48y = 32x - 26x

4y = 6x   |:2

2y = 3x      

x/y = 2/3

d)

5x + 3y/2x + 3y = 58/34   |:2

5x + 3y/2x + 3y = 29/17  

29(2x + 3y) = 17(5x + 3y)

58x + 87y = 85x + 51y

87y  - 51y = 85x - 58x

36y = 27x  |:9

4y = 3x

3x = 4y

x/y = 4/3

(e)

(7x + 2y)/(4x + 7y) = 11/18

11·(4x + 7y) = 18·(7x + 2y)

44x + 77y = 126x + 36y

77y - 36y = 126x - 44x

41y = 82x   |:41

y = 2x

2x = y

x/y = 1/2

(f)

(3x + y)/(4x + 3y) = 9/17

17·(3x + y) = 9·(4x + 3y)

51x + 17y = 36x + 27y

15x = 10y   |:5

3x = 2y

x/y = 2/3

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