30% of paintings were by Picasso, 25% by Renoir. If 24 were Picasso's, how many were Renoir's?
Renoir painted 20 paintings.
Given that 30% of the paintings were by Picasso and that corresponds to 24 paintings, we can calculate the total number of paintings. If 30% equals 24, then 100% (the total) can be found by dividing 24 by 0.30, resulting in 80 total paintings. Since 25% of these were by Renoir, 25% of 80 equals 20, confirming that Renoir painted 20 paintings.
This choice represents the correct calculation based on the total number of paintings. With a total of 80 paintings and Renoir accounting for 25%, the calculation (0.25 × 80) yields 20 paintings, thereby confirming this as the correct answer.
This option incorrectly suggests that Renoir painted 18 paintings. To arrive at this number, one would have to miscalculate the percentage of the total or misinterpret the total number of paintings. The correct percentage calculation based on the total number of 80 does not support this figure.
Choosing 12 as the number of paintings by Renoir reflects a misunderstanding of the percentage breakdown. To get 12 from a total of 80 would imply Renoir painted only 15%, which contradicts the given information that 25% of the total was attributed to him.
This choice indicates that Renoir only painted 6 artworks, which represents a drastic underestimation. Such a figure would correspond to only 7.5% of the total, which is far less than the stated 25%, thus misaligning with the problem's parameters.
The calculations confirm that Renoir's contribution of 20 paintings accurately reflects the stated 25% of the total of 80 paintings. The other options misrepresent the relationship between the percentages and the total number, showcasing common errors in percentage interpretation. Understanding these calculations is crucial for accurately solving problems involving proportions and percentages in various contexts.
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