Mathematics
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?
Polynomials
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Answer
Let the smaller number be x.
Then, the larger number = 5x.
After adding 21 to both:
New smaller number = x + 21
New larger number = 5x + 21
According to the question, after adding 21, one of the new numbers becomes twice the other.
Since 5x + 21 > x + 21, the larger new number is twice the smaller new number.
So,
5x + 21 = 2(x + 21)
⇒ 5x + 21 = 2x + 42
⇒ 5x - 2x = 42 - 21
⇒ 3x = 21
⇒ x =
⇒ x = 7
So,
Smaller number = 7
Larger number = 5 × 7 = 35
Hence, the two numbers are 7 and 35.
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