Two numbers are in the ratio 5 : 7 and their sum is 144. Find the numbers.

Question

Accepted Answer

Solution:
Let the two numbers be:
$$ 5x 	ext{ and } 7x $$
According to the question:
$$ 5x + 7x = 144 $$
$$ 12x = 144 $$
$$ x = \frac{144}{12} $$
$$ x = 12 $$
Now, the numbers are:
$$ 5x = 5 	imes 12 = 60 $$
$$ 7x = 7 	imes 12 = 84 $$
Therefore, the two numbers are:
$$ \boxed{60 	ext{ and } 84} $$

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