Let's define the variables first:
- Let \( x \) be the number of light clothes.
- The number of dark clothes is then \( 2x + 3 \).
According to the problem, the total number of clothes is the sum of dark and light clothes:
\[ \text{Total clothes} = x + (2x + 3) = 3x + 3 \]
We are given that 60% of the clothes are dark. This can be expressed as:
\[ \frac{\text{Number of dark clothes}}{\text{Total clothes}} = 0.6 \]
Substituting the expressions for the number of dark clothes and the total clothes into this equation, we have:
\[ \frac{2x + 3}{3x + 3} = 0.6 \]
To convert the decimal to a fraction:
\[ 0.6 = \frac{60}{100} \]
Now we can equate this to the left side:
\[ \frac{2x + 3}{3x + 3} = \frac{60}{100} \]
Next, we cross-multiply to eliminate the fraction:
\[ 100(2x + 3) = 60(3x + 3) \]
Now, if we analyze the options given in the question:
- \( \frac{x}{2x + 3} = \frac{40}{60} \)
- \( \frac{x}{2x + 3} = \frac{60}{40} \)
- \( \frac{x}{2x + 3} = \frac{40}{100} \)
- \( \frac{x}{2x + 3} = \frac{60}{100} \)
Given our equation from the problem, it would actually lead us to:
\[ \frac{2x + 3}{3x + 3} = \frac{60}{100} \]
However, we are looking for the equivalent form. We can write:
\[ \frac{x}{2x + 3} = \text{some ratio} \]
But we want to focus on the equivalent proportion:
Since \( \frac{60}{100} \) can also be expressed as \( \frac{60/60}{100/60} \), we find that:
\[ \frac{60}{100} = \frac{60/60}{100/60} = \frac{60}{100} \rightarrow \frac{60}{100} \sim 0.6 \]
So from our derivation:
The correct proportional relationship leads us to option 4:
\[ \frac{x}{2x + 3} = \frac{60}{100} \]
Therefore, the best equation to represent the scenario is:
4. \( \frac{x}{2x + 3} = \frac{60}{100} \)
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