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?
Answers
Answer:
Given :-
- A positive number is 5 times another number.
- 21 is added to both the numbers, then one of the new numbers becomes twice the other new number.
To Find :-
- What are the numbers.
Solution :-
Let,
➲ First Number = y
➲ Second Number = 5y
Now,
◆ 21 is added to both the numbers :
➟ First Number = y + 21
➟ Second Number = 5y + 21
According to the question,
↦ 5y + 21 = 2(y + 21)
↦ 5y + 21 = 2y + 42
↦ 5y - 2y = 42 - 21
↦ 3y = 21
↦ y = 21/3
↦ y = 7/1
➠ y = 7
Hence, the required numbers are :
❒ First Number :
⇒ First Number = y
➦ First Number = 7
❒ Second Number :
⇒ Second Number = 5y
⇒ Second Number = 5(7)
⇒ Second Number = 5 × 7
➦ Second Number = 35
∴ The numbers are 7 and 35 .
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VERIFICATION :-
➞ 5y + 21 = 2(y + 21)
By putting y = 7 we get,
➞ 5(7) + 21 = 2(7 + 21)
➞ 35 + 21 = 2(28)
➜ 56 = 56
Hence, Verified.
Solution :
• A positive number is 5 times another number.
• It 21 is added to both the numbers, one of the new numbers becomes twice the other new number.
We have to find these numbers.
Let us assume that the smaller number is x.
Then the other number is 5x .
21 is added to both the numbers.
New number 1 = x + 21
New number 2 = 5x + 21
New Number 2 = 2 × ( New number 1)
> 5x + 21 = 2(x + 21)
> 5x + 21 = 2x + 42
> 3x = 21
> x = 7.
Answer : The two numbers are 7 and 35 respectively.
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