What should be added to each term of the ratio $5 : 11$ so that the ratio becomes $3 : 5$?

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Accepted Answer

**Solution:**

1. Let the number to be added to each term be $x$.

2. The original ratio is $5 : 11$. After adding $x$ to both terms, the new ratio becomes:
   $$\frac{5 + x}{11 + x} = \frac{3}{5}$$

3. Cross-multiply to solve for $x$:
   $$5(5 + x) = 3(11 + x)$$
   $$25 + 5x = 33 + 3x$$

4. Rearranging terms:
   $$5x - 3x = 33 - 25$$
   $$2x = 8$$
   $$x = 4$$

**Answer:** $4$

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