Question - Calculating Total Area for Painting Walls
Solution:
The question asks which statement shows how to find the total area that the workers need to paint.The formula to calculate the area of a wall is given as Area = length x width.According to the problem, there are two sets of walls that need to be painted:- 5 walls that are 16 meters long and 4 meters high.- 6 walls that are 24 meters long and 4 meters high.Now let's calculate the area of each type of wall and then total them up:For the 5 walls that are 16 meters by 4 meters:Area for one wall = 16 x 4.Total area for these 5 walls = 5 x (16 x 4).For the 6 walls that are 24 meters by 4 meters:Area for one wall = 24 x 4.Total area for these 6 walls = 6 x (24 x 4).To get the total area to paint, we add the areas for both sets of walls:Total area = 5 x (16 x 4) + 6 x (24 x 4).Now we can look at the options provided to see which one matches our equation.Option A: $$ A = 5 \cdot (16 + 4) + 6 \cdot (24 + 4) $$ — This is incorrect because it improperly adds the length and width rather than multiplying them.Option B: $$ A = 5 \cdot 16 + 4 + 6 \cdot 24 + 4 $$ — This is incorrect because it does not group the multiplication properly and adds 4 incorrectly at the end.Option C: $$ A = 5 \cdot (16 \cdot 4) + 6 \cdot (24 \cdot 4) $$ — This matches our correct equation for the total area to be painted.Option D: $$ A = 3 \cdot (16 \cdot 24 \cdot 4) $$ — This is incorrect because it combines the numbers in a way that does not represent the problem's scenario.The correct option is therefore C: $$ A = 5 \cdot (16 \cdot 4) + 6 \cdot (24 \cdot 4) $$.
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