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

Step-by-step explanation:

Let,

• Other number = x
• Positive number = 5x

When added 21 to both numbers,

• Other number = x + 21
• Positive number = 5x + 21

A/C,

2(x + 21) = 5x + 21

Multiplying x and 21 from 2

⟹ 2x + 42 = 5x + 21

Transposing 5x to LHS and 42 to RHS

⟹ 2x - 5x = 21 - 42

On subtracting, we get

⟹ -3x = -21

Eliminating -ve sign from both sides and dividing

⟹ x = 21/3

Cancelling to get 7

⟹ x = 7

Therefore,

• Other number = x = 7.
• Positive number = 5x = 5×7 = 35.

Answer 2

☆ Given :-

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

☆ To Find :-

• The two numbers

⠀

☆ Let :-

• The positive number be x
• And other number be 5x

Now, According to the question,

$\sf: \implies \: 2(x + 21) = 5x + 21 \\ \sf: \implies \:2x + 42 = 5x + 21 \: \: \: \: \\ \sf: \implies \:2x - 5x = 21 - 42 \: \: \: \: \\ \sf: \implies \: 2(x + 21) = 5x + 21 \\ \sf: \implies \:2x + 42 = 5x + 21 \: \: \: \: \\ \sf: \implies \: - 3x = - 21 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf: \implies \: 2(x + 21) = 5x + 21 \\ \sf: \implies \:2x + 42 = 5x + 21 \: \: \: \: \\ \sf: \implies \:x = \frac{ - 21}{ - 3} = 7 \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Therefore,

$\sf: \implies \: the \: positive \: number \: = x = 7 \: \: \: \: \: \: \: \\ \sf: \implies \: and \: other \: number \: = 5 \times 7 = 35$