Question

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

Answer 1

Solution :

Let the greater number be x and the smaller number be y.

According to the first condition, two numbers differ by 3.

x - y = 3 ...... (I)

According to the second condition, the sum of twice the smaller number and thrice the greater number is 19.

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

Multiplying equation (i) by 2, we get

2x - 2y = 6 ..... (iii)

Adding equations (ii) and (iii), we get

⠀3x + 2y = 19

+ 2x - 2y = 6

------------------------

⠀5x ⠀⠀⠀= 25

x = 25/5

x = 5

Substituting x = 5 in equation (i), we get

x - y = 3

5 - y = 3

5 - 3 = y

y = 2

∴ The required numbers are 5 and 2.

Answer 2

Answer:

Let the Smaller Number be a and Greater Number be (a + 3).

• According to the Question Now :

The sum of twice the smaller number and thrice the greater number is 19.

⇒ (2 × Smaller No.) + (3 × Greater No.) = 19

⇒ 2a + 3(a + 3) = 19

⇒ 2a + 3a + 9 = 19

⇒ 2a + 3a = 19 - 9

⇒ 5a = 10

• Dividing both term by 5

⇒ a = 2

• Required Numbers are :

◗ Smaller No. = a = 2

◗ Greater No. = (a + 3) = 5