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ᴀ ꜰʀᴀᴄᴛɪᴏɴ ʙᴇᴄᴏᴍᴇꜱ 9/11, ɪꜰ 2 ɪꜱ ᴀᴅᴅᴇᴅ ᴛᴏ ʙᴏᴛʜ ᴛʜᴇ ɴᴜᴍᴇʀᴀᴛᴏʀ ᴀɴᴅ ᴛʜᴇ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ. ɪꜰ 3 ɪꜱ ᴀᴅᴅᴇᴅ ᴛᴏ ʙᴏᴛʜ ᴛʜᴇ ɴᴜᴍᴇʀᴀᴛᴏʀ ᴀɴᴅ ᴛʜᴇ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ, ɪᴛ ʙᴇᴄᴏᴍᴇꜱ 5/6. ꜰɪɴᴅ ᴛʜᴇ ꜰʀᴀᴄᴛɪᴏɴ.​

Answer 1

Step-by-step explanation:

Let the fraction be x/y

(x+2)/(y+2) = 9/11

cross multiplication

11(x+2) = 9(y+2)

11x + 22 = 9y + 18

11x + 22 - 18 = 9y

11x + 4 = 9y

11x + 4 - 9y = 0

or

11x -9y + 4 = 0 (eqn. no. 1)

(x+3)/(y+3) = 5/6

cross multiplication

6(x+3) = 5(y+3)

6x + 18 = 5y + 15

6x + 18 - 15 = 5y

6x + 3 = 5y

6x + 3 - 5y = 0

or

6x - 5y + 3 = 0 (eqn. no. 2)

first equal the value of x or y in both the eqns.

multiplying eqn. no. 1 by 5

= 5( 11x -9y + 4 = 0 )

= 55x - 45y + 20 = 0 (eqn. no. 3)

multiplying eqn. no. 2 by 9

= 9( 6x - 5y + 3 = 0 )

= 54x - 45y + 27 = 0 (eqn. no. 4)

Now, the value of y is same in both the eqns

Now eliminating y by subtracting eqn. no. 4 from eqn. no. 3

55x - 45y + 20 = 0 - (54x - 45y + 27 = 0)

55x - 45y + 20 - 54x + 45y - 27 = 0

(55x - 54x - 45y + 45y + 20 - 27 = 0)

x + 0 - 7 = 0

x - 7 = 0

x = 7

now, putting the value of x = 7 in eqn. no. 1

11x -9y + 4 = 0

11(7) - 9y + 4 = 0

77 - 9y + 4 = 0

81 - 9y = 0

81 = 9y

9y = 81

y = 81/9

y = 9

Hence, x/y = 7/9

So, the fraction is 7/9.

Answer 2

Answer :

• Jacob's present age = 40 years

• Jacob's son's present age = 10 years

Solution :

Given :

• After five years, the age of Jacob will be three times that of his son.

• Five years ago, Jacob's age was seven times that of his son.

To find :

• The present age of Jacob

• The present age of Jacob's son

Required Solution :

Let,

• The present age of Jacob = x years

• The present age of Jacob's son = y years

Their ages after five years :

= Jacob's age after 5 years = x + 5 years

= Jacob's son's age after 5 years = y + 5 years

According to the first condition given,

= Jacob's age = 3(Jacob's son's age)

= x + 5 = 3(y + 5)

= x + 5 = 3y + 15

= x - 3y = 15 - 5

= x - 3y = 10 -----(1)

Their ages before 5 years :

= Jacob's age before 5 years = x - 5 years

= Jacob's son's age before 5 years = y - 5 years

According to the second condition given,

= Jacob's age = 7(Jacob's son's age)

= x - 5 = 7(y - 5)

= x - 5 = 7y - 35

= x - 7y = - 35 + 5

= x - 7y = - 30 ------(2)

Solving (1) and (2) :

⠀⠀⠀⠀⠀⠀⠀⠀x - 3y = 10

⠀⠀⠀⠀⠀⠀⠀⠀x - 7y = - 30

⠀⠀⠀⠀⠀⠀⠀⠀-⠀+⠀⠀⠀+

⠀⠀⠀⠀⠀⠀______________

⠀⠀⠀⠀⠀⠀⠀⠀⠀4y = 40

⠀⠀⠀⠀⠀⠀______________

= 4y = 40

= y = 40/4

= y = 10

The value of y = 10

Substituting the value of y in equation (1) ::

= x - 3y = 10

= x - 3(10) = 10

= x - 30 = 10

= x = 10 + 30

= x = 40

The value of x = 40

The age of Jacob and his son :

⇒ Jacob's present age = x years

⇒ Jacob's present age = 40 years

⇒ Jacob's son's present age = y years

⇒ Jacob's son's present age = 10 years