Question

A positive number is three times the another number. If 21 is added to the both numbers ,then one of the new numbers become twice the other new number. What are the numbers?​

Answer 1

Let the number be M.

A positive number is three times another number.

Therefore, a positive number is 3M.

If 21 is added to both numbers, then one of the new numbers become twice the other new number.

Now,

New number (other) = M + 21

New positive number = 3M + 21

According to question,

⇒ 3M + 21 = 2(M + 21)

⇒ 3M + 21 = 2M + 42

⇒ 3M - 2M = 42 - 21

⇒ M = 21

Positive number = 3(21) = 63

Therefore,

The other number is 21 and a positive number is 63.

Verification:

From the above calculations, we have M = 21

Substitute value of M in 3M + 21 = 2(M + 21)

⇒ 3(21) + 21 = 2(21 + 21)

⇒ 63 + 21 = 2(42)

⇒ 84 = 84

Answer 2

Step-by-step explanation:

Given -

• A positive integer is three times the another number.

To Find -

What are the numbers ?

Let x be the number.

Then,

Other number is 3x.

Now,

According to the question

• If 21 is added to both the numbers.

Then,

The numbers are x + 21 and 3x + 21

As Given -

One of the number become twice the other number.

It means,

= 3x + 21 = 2(x + 21)

= 3x + 21 = 2x + 42

= 3x - 2x = 42 - 21

• = x = 21

Hence,

One number is 21

and

Other number is 3x = 3(21) = 63

Verification -

= 3x + 21 = 2(x + 21)

= 3(21) + 21 = 2(21 + 21)

= 63 + 21 = 2 × 42

= 84 = 84

Hence,

Verified..