Question

the positive number is 5 times another number if 21 is added to both the number then one of the new number becomes twice the other number find the two number

Answer 1

Hey mate!!

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Let x be the first number and let y be the second number. From the first statement, we have:

x = 5y.

From the second statement, we have:

x + 21 = 2 × (y + 21).

[Since x = 5y, x must be greater than y, so x + 21 must be greater than y+ 21. That's how we know x + 21 = 2 × (y + 21), rather than the other way around, y + 21 = 2 × (x + 21).]

So all we have to do is solve this system of equations. This can be done easily by substitution, since the first equation is already solved for x. Plugging in 5y for x in the second equation, we have:

5y + 21 = 2 × (y + 21)

5y + 21 = 2y + 42

3y + 21 = 42

3y = 21                       

y = 7                            

Thus, y = 7

And x = 5y = 5 × 7 = 35,

so the two numbers are 7 and 35. 

Thanks for the question!!

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Answer 2

Define x:

Let the number be x

The other number is 5x

Solve x:

5x + 21 = 2(x + 21)

5x + 21 = 2x + 42

3x = 21

x = 7

Find the numbers:

one number = x = 7

The other number = 5x = 5(7) = 35

Answer: The two numbers are 7 and 35.