Question

(2) A positive number is 5 times another number. If 21 is added to both the numbers, then one of the new numbers becomes twice the other new number. What are the numbers?

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Answer 1

Answer: the numbers are 7 and 35

Step-by-step explanation: let the numbers be x and 5x

now the equation will be 2(x+21) = 5x+21

2x+42= 5x+21

2x= 5x+21-42

2x= 5x-21

-3x= -21

x= 7

5x = 5(7) = 35

Answer 2

Given:

• A positive number is 5 times another number.
• if 21 is added to both the numbers then one of the new numbers becomes twice the other new number

To Find:

• The New numbers.

Solution :

Now,

• Let the another number be "x"

According to Question

• First Number = 5x

Now, According to Question again

$\sf:\implies\: x + 21 = 5x + 21$

$\sf:\implies\: 2 ( x + 21 ) = 5x + 21$

$\sf:\implies\: 2x + 42 = 5x + 21$

$\sf:\implies\: 2x - 5x = 21 - 42$

$\sf:\implies\: - 3x = - 21$

$\sf:\implies\: 3x = 21$

$\sf:\implies\: x = \frac{21}{3}$

$\sf:\implies\: \red{ x = 7}$

Therefore, The Value of x is 7.

• First Number = 5x → 5 × 7 = 35

• Another Number = x = 7.

The Numbers are 35 and 7 Respectively.

VERIFICATION:-

if 21 is added to both the numbers then one of the new numbers becomes twice the other new

$\sf:\implies\: 7 + 21 = 35 + 21$

$\sf:\implies\: 2 ( 7 + 21 ) = 35 + 21$

$\sf:\implies\: 14 + 42 = 35 + 21$

$\sf:\implies\red {56 = 56.}$

hence VERIFIED