Question

Please help me solving all

Answer 1

Question 1 :

Let the two no.s be x and 2 x.

x + 2 x = 60

= > 3 x = 60

= > x = 20

Hence no.s are 20 and 40

ANSWER : 20 and 40

Question 2 :

3 + 2x = 5/x

= > 3 x + 2 x² = 5

= > 2 x² + 3 x - 5 = 0

= > 2 x² - 2 x + 5 x - 5 =0

= > 2 x ( x - 1 ) + 5 ( x - 1 ) =0

x - 1 = 0

or 2 x + 5 = 0

x = 1 or x = -5/2

ANSWER : 1 or -5/2

Question 3 :

Let no. be x .

x + 32 = 3 x

= > 2 x = 32

= > x = 16

ANSWER : The number is 16 .

Question 4 :

Let no.s be x and x+1

x + x + 1 = 55

= > 2 x + 1 = 55

= > 2 x = 54

= > x = 27

x + 1 = 28

28 is greater

ANSWER :  28

Question 5 :

Let the no. be x

2 x  + 12 = 50

= > 2 x = 50 - 12

= > 2 x = 38

= > x = 38/2

= > x = 19

ANSWER :

19

Question 6 :

Let no.s be x , x + 2 , x + 4

x + x + 2 + x + 4 = 225

= > 3 x = 225-6

= > 3 x = 219

= > x = 73

x + 2 = 75

x + 4 = 77

ANSWER : 73 , 75 , 77.

Question 7 :

The no.s are x , x + 3 , x + 6

x + x + 3 + x + 6 = 315

= > 3 x = 315-9

= > x = 306/3

= > x = 102

ANSWER 102, 105 , 108

Question 9 :

Let the fraction be ( x - 7 ) / x

According to problem :

( x - 7 )/x = ( x - 7 + 2 ) / ( x + 9 )

= > ( x - 7 ) ( x + 9 ) = x ( x -  5 )

= > x² - 7 x + 9 x - 63 = x² - 5 x

= > x² - 2 x - 63 = x² - 5 x

= > 3 x = 63

= > x = 63/3

= > x  = 21

Fraction = ( 21 - 7 ) / 21 = 14/21

ANSWER : 14/21

Answer 2

Hello !

Q: 1 :

Solution:

Let the two number be k and 2k.

k + 2k = 60

⇒ 3k = 60

⇒ k = 20

Therefore, 2 numbers are 20 and 40

Q: 2 :

Solution:

3 + 2k = 5/k

= > 3k + 2k² = 5

= > 2k² + 3k - 5 = 0

= > 2k² - 2k + 5k - 5 =0

= > 2k ( k - 1 ) + 5 ( k - 1 ) =0

k - 1 = 0

or, 2k + 5 = 0

k = 1 or k = -5/2

Q: 3 :

Solution:

Let no. be k .

k + 32 = 3k

= > 2k = 32

= > k = 16


Hence, The number is 16 .


Q: 4 :

Solution:

Let no.s be k and k+1

k + k + 1 = 55

= > 2k + 1 = 55

= > 2k = 54

= > k = 27

k + 1 = 28

Hence, 28 is greater


Q: 5 :

Solution:

Let the no. be k

2k  + 12 = 50

= > 2k = 50 - 12

= > 2k = 38

= > k = 38/2

= > k = 19

Hence, the number is 19


Q:6 :

Let numbers be k , k + 2 , k + 4


k + k + 2 + k + 4 = 225

= > 3k = 225-6

= > 3k = 219

= > k = 73

k + 2 = 75

k + 4 = 77

Hence, the numbers are: 73 , 75 and , 77.

Q: 7 :

Solution:

The numbers be k , k + 3 , k + 6

k + k + 3 + k + 6 = 315

= > 3k = 315-9

= > k = 306/3

= > k = 102

Hence, numbers are 102, 105 and , 108

Q: 9 :

Solution:

Let the fraction be ( k - 7 ) / k

According to problem :

( k - 7 )/k = ( k - 7 + 2 ) / ( k + 9 )

= > ( k - 7 ) ( k + 9 ) = k ( k -  5 )

= > k² - 7 k + 9 k - 63 = k² - 5 k

= > k² - 2 k - 63 = k² - 5 k

= > 3 k = 63

= > k = 63/3

= > k  = 21

Hence, Fraction is ( 21 - 7 ) / 21 = 14/21