Question

Two numbers differ by 3.The sum of twice the smaller and thrice the greater number is 19. find the numbers ​

Answer 1

Answer:

The required numbers are 5 and 2.

Step-by-step-explanation:

Let the greater number be x.

And the smaller number be y.

From the first condition,

$\boxed{x - y = 3}$ ... ( 1 )

Thrice the greater number = 3 × x = 3x

Twice the smaller number = 2 × y = 2y.

From the second condition,

$\boxed{3x + 2y = 19}$ .... ( 2 )

Multiplying equation ( 1 ) by 2,

$\boxed{2x - 2y = 6}$ ... ( 3 )

Adding equations ( 2 ) and ( 3 ),

3x + 2y = 19 ... ( 2 )

+ 2x - 2y = 6 ... ( 3 )

____________

5x = 25

$\therefore$ $\boxed{x = 5}$

Substituting x = 5 in equation ( 1 ),

x - y = 3

$\therefore$ 5 - y = 3

$\therefore$ - y = 3 - 5

$\therefore$ - y = - 2

$\therefore$ $\boxed{y = 2}$

Ans.: The required numbers are 5 and 2.

Verification:

From the first condition,

x - y = 3

$\therefore$ LHS = 5 - 2

$\therefore$ LHS = 3

RHS = 3

$\therefore$ $\boxed{LHS = RHS}$

Now, from second condition,

3x + 2y = 19

$\therefore$ LHS = ( 3 × 5 ) + ( 2 × 2 )

$\therefore$ LHS = 15 + 4

$\therefore$ LHS = 19

RHS = 19

$\therefore$ $\boxed{LHS = RHS}$

Hence verified!

Answer 2

Answer:

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