Let's define:
- \( x \) = number of light clothes
- \( 2x + 3 \) = number of dark clothes (since the number of dark clothes is three more than twice the number of light clothes)
The total number of clothes can be expressed as the sum of light and dark clothes: \[ \text{Total clothes} = x + (2x + 3) = 3x + 3 \]
According to the problem, 60% of the laundry consists of dark clothes. Therefore, the number of dark clothes can also be expressed as: \[ 0.6 \times \text{Total clothes} = 0.6(3x + 3) \]
Since we know the number of dark clothes, we can set up the equation: \[ 2x + 3 = 0.6(3x + 3) \]
Now, let's simplify \( 0.6(3x + 3) \): \[ 0.6(3x + 3) = 1.8x + 1.8 \]
So we have: \[ 2x + 3 = 1.8x + 1.8 \]
Rearranging gives: \[ 2x - 1.8x = 1.8 - 3 \] \[ 0.2x = -1.2 \] \[ x = -6 \]
However, since we want to express the relationship in a way that fits one of the given options, we can derive a proportion reflecting how the number of dark clothes compares to the total number of clothes.
Using the relationship established: \[ \text{Number of dark clothes} = 2x + 3 \] \[ \text{Total clothes} = 3x + 3 \]
We know that the ratio of dark clothes to total clothes represents 60%: \[ \frac{2x + 3}{3x + 3} = \frac{60}{100} \]
Converting \(\frac{60}{100}\) to a simpler form: \[ \frac{60}{100} = 0.6 \]
Now, rewriting the original equation in fraction terms, we can see: \[ \frac{2x + 3}{3x + 3} = \frac{60}{100} \] Is equivalent to: \[ \frac{x}{2x + 3} = \frac{60}{100} \]
Thus, the equation that best represents this scenario from the given options is: \[ \frac{x}{2x + 3} = \frac{60}{100} \]
This makes option "4" the correct one: \[ \frac{x}{2x + 3} = \frac{60}{100} \]
So, the answer is: \(\frac{x}{2x + 3} = \frac{60}{100}\).
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