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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?
Given:
A Positive number is 5 times another number and if 21 is added to both the numbers, then one of the new numbers becomes twice the other new number.
To do:
We have to find the numbers.
Solution:
Let the smaller number be $a$
This implies,
The other number $= 5a$
Adding $21$ to both numbers, we get,
Smaller number $= a + 21$
Other number $= 5a + 21$
According to the question,
Bigger number $= 2 \times$ Smaller number
$5a + 21 = 2 \times (a + 21)$
$5a + 21 = 2a + 42$
$5a - 2a = 42 - 21$
$3a = 21$
$a = \frac{21}{3}$
$a = 7$
Therefore,
The smaller number $a=7$
The other(bigger) number $= 5a$
$= 5 \times 7$
$=35$
The required numbers are $7$ and $35$.
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