Question

The sum of two numbers is 19. The difference between twice the smaller and the larger is 8. What are the numbers?

Answer 1

Answer:-

Smaller number = 9

larger number = 10.

Explanation:-

let the smaller number be "x" and larger number be "y".

Sum = 19

x + y = 19 __ equation-(1)

Difference between twice the smaller and larger = 8.

2x - y = 8 __ equation -(2)

Add both the equations,

x + y + 2x - y = 19+8

3x = 27

x = 27/3

x = 9.

Substitute the value of "x" in equation -(1)

x + y = 19

9 + y = 19

y = 19 - 9

y = 10.

Therefore, the smaller number (x) = 9 and Larger number (y) = 10.

Answer 2

Given :

• The sum of two numbers is 19.
• The difference between twice the smaller and the larger is 8.

To Find :

• The numbers.

Solution :

Let the greater number be x.

Let the smaller number be y.

Case 1 :

$\sf{Greater\:Number\:+\:Smalller\:Number\:=\:19}$

Equation :

$\pink{\implies}$ $\sf{x+y=19}$

$\sf{x=19-y}$ ____(1)

Case 2 :

$\sf{2(smaller\:number)\:-\:(greater\:number)\:=8}$

Equation :

$\pink{\implies}$ $\sf{2(y)-x=8}$

$\pink{\implies}$ $\sf{2y-x=8}$

$\pink{\implies}$ $\sf{2y-(19-y) =8}$

$\pink{\implies}$ $\sf{2y-19+y=8}$

$\pink{\implies}$ $\sf{2y+y=8+19}$

$\pink{\implies}$ $\sf{3y=27}$

$\pink{\implies}$ $\sf{y=\cancel{\dfrac{27}{3}}}$

$\pink{\implies}$ $\sf{y=9}$

Substitute, y = 9 in equation (1),

$\pink{\implies}$ $\sf{x=19-y}$

$\pink{\implies}$ $\sf{x=19-9}$

$\pink{\implies}$ $\sf{x=10}$

$\large{\boxed{\sf{\red{Greater\:number\:=\:x\:=\:10}}}}$

$\large{\boxed{\sf{\red{Smaller\:number\:=\:y\:=\:9}}}}$