Uche is a cartographer. He picks a scale to fit a map of India onto a page of an atlas. The page is 12 by 12 inches, with 0.75 inch margins on all 4 sides. India measures 3,214 kilometers from north to south and 2,933 kilometers from west to east. Uche wants the longest dimension of India to fit exactly in between the margins of the page. If k is the number of kilometers per inch in Uche's scale, which equation best models the situation?Choose 1 answer:(A) 12k=3,214(B) 12k=2,933(C) 10.5k=2,933(D) 10.5k=3,214
Q. Uche is a cartographer. He picks a scale to fit a map of India onto a page of an atlas. The page is 12 by 12 inches, with 0.75 inch margins on all 4 sides. India measures 3,214 kilometers from north to south and 2,933 kilometers from west to east. Uche wants the longest dimension of India to fit exactly in between the margins of the page. If k is the number of kilometers per inch in Uche's scale, which equation best models the situation?Choose 1 answer:(A) 12k=3,214(B) 12k=2,933(C) 10.5k=2,933(D) 10.5k=3,214
Calculate Usable Space: Uche has a page that is 12×12 inches, but we need to account for the margins. Since there is a 0.75 inch margin on all 4 sides, we need to subtract this margin from each dimension to find the usable space. The total margin to subtract from each dimension is 0.75 inches ×2 (for both sides of the page).Calculation: 12 inches - (0.75 inches ×2) = 12 inches - 1.5 inches = 0.750 inches.
Determine Longest Dimension: Now we need to determine which dimension of India is the longest to fit it within the 10.5 inches of usable space. We compare the north-to-south length (3,214 km) with the west-to-east length (2,933 km).Calculation: 3,214 km is greater than 2,933 km, so the north-to-south dimension is the longest.
Find Scale Factor: Since the longest dimension of India (3,214km) must fit into the 10.5inches of usable space on the page, we set up the equation to find the scale k, which is the number of kilometers per inch.Calculation: 10.5inches×k=3,214km.
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