Verified answer

Answer:

Largest Number = a = 7

Smallest Number = b = 4

Step-by-step explanation:

Largest Number = a

Smallest Number = b

a + b = 11

a + 2b = 15

(a + 2b) - (a + b) = 15 - 11

a + 2b - a - b = 15 - 11

b = 4

a + b = 11

a + 4 = 11

a = 11 - 4

a = 7

Answer:

The required numbers are 4 & 7.

Step-by-step-explanation:

Let the smaller number be x.

And the greater number be y.

From the first condition,

Sum of two numbers is 11.

∴ x + y = 11

⇒ x = 11 - y - - - ( 1 )

From the second condition,

Sum of twice the smaller number & greater number is 15.

∴ 2y + x = 15

⇒ 2y + ( 11 - y ) = 15 - - - [ From ( 1 ) ]

⇒ 2y + 11 - y = 15

⇒ 2y - y = 15 - 11

⇒ y = 4

By substituting y = 4 in equation ( 1 ), we get,

x = 11 - y - - - ( 1 )

⇒ x = 11 - 4

⇒ x = 7

∴ The required numbers are 4 & 7.