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Dropdown 1: 4
Dropdown 2: 30,000 acres more
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Difficulty:
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29% (03:39) correct
71%
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wrong
based on 363
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The graph shows the percent change in the area of different land cover types across five states (DE, MD, PA, VA, and WV) from 1982 to 1997.
Select from each drop-down menu the option that creates the most accurate statement based on the information provided.
If the combined rural area of Pennsylvania (PA) and Virginia (VA) was twice that of the pasture area in West Virginia (WV) in 1982, then in 1997, the combined rural area of Pennsylvania (PA) and Virginia (VA) was approximately times larger than the pasture area in West Virginia.
If Delaware (DE) had 380,000 acres of cropland in 1997 and Maryland (MD) had 500,000 acres of cropland in 1997, then Delaware had approximately cropland than Maryland in 1982.
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Official Answer
Dropdown 1: 4
Dropdown 2: 30,000 acres more
18 Nov 2024, 10:19
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Bunuel
Official Solution:
Drop-down 1:
Assuming the combined rural area of Pennsylvania (PA) and Virginia (VA) was 100 \(unit^2\) in 1982, the pasture area in West Virginia (WV) would be 50 \(unit^2\) in the same year. From the graph, we see that the rural areas of both Pennsylvania (PA) and Virginia (VA) increased by 40%, so in 1997, the combined rural area would become 140 \(unit^2\). Meanwhile, the pasture area in West Virginia (WV) decreased by 25%, reducing it to 37.5 \(unit^2\). Therefore, in 1997, the combined rural area of Pennsylvania (PA) and Virginia (VA) was \(\frac{140}{37.5} \approx 4\) times larger than the pasture area in West Virginia.
Drop-down 2:
Delaware's cropland decreased by 35% from 1982 to 1997, so 380,000 acres of cropland in 1997 implies that in 1982 it was \(\frac{380,000}{0.65} \approx 585,000\) acres. During the same period, Maryland's (MD) cropland decreased by 10%, so 500,000 acres of cropland in 1997 implies that in 1982 it was \(\frac{500,000}{0.90} \approx 555,000\) acres. Therefore, in 1982, Delaware had approximately 30,000 acres more cropland than Maryland.
Correct answer:
Dropdown 1: "4"
Dropdown 2: "30,000 acres more"
23 Dec 2024, 18:27
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1. Let the pasture area of West Virginia before and after be \(W_1\) and \(W_2\). Also let the rural areas of Pennsylvania and Virginia before and after be \(P_1\), \(P_2\), \(V_1\), and \(V_2\), respectively.
2. It is known that \(2W_1 = P_1 + V_1\).
3. From the charts it can be deduced: \((1 - 0.25) * W_1 = W_2\), \((1 + 0.4) * P_1 = P_2\), and \((1 + 0.4) * V_1 = V_2\).
4. The question asks us to find the value of \(\frac{P_2 + V_2}{W_2}\). It can be simplified into \(\frac{P_2 + V_2}{W_2} = \frac{1.4P_1 + 1.4V_1}{0.75W_1} = \frac{1.4(P_1 + V_1)}{0.75 * 0.5(P_1 + V_1)} \approx 3.73\), which is closest to 3.5.
5. Let the cropland area of Delaware and Maryland before and after be \(D_1\), \(D_2\), \(M_1\), and \(M_2\), respectively.
6. It is known that \(D_2 = 380000\) and \(M_2 = 500000\).
7. From the charts it can be deduced: \((1 - 0.35)D_1 = D_2 \rightarrow D_1 = \frac{380000}{0.65} \approx 584615\) and \((1 - 0.1)M_1 = M_2 \rightarrow M_1 = \frac{500000}{0.9} \approx 555555\).
8. The questions asks to find \(D_1 - M_1 = 584615 - 555555 = 29060\), which is about 30000 acres more.
9. Our answer will be: 3.5 and "30000 acres more."
2. It is known that \(2W_1 = P_1 + V_1\).
3. From the charts it can be deduced: \((1 - 0.25) * W_1 = W_2\), \((1 + 0.4) * P_1 = P_2\), and \((1 + 0.4) * V_1 = V_2\).
4. The question asks us to find the value of \(\frac{P_2 + V_2}{W_2}\). It can be simplified into \(\frac{P_2 + V_2}{W_2} = \frac{1.4P_1 + 1.4V_1}{0.75W_1} = \frac{1.4(P_1 + V_1)}{0.75 * 0.5(P_1 + V_1)} \approx 3.73\), which is closest to 3.5.
5. Let the cropland area of Delaware and Maryland before and after be \(D_1\), \(D_2\), \(M_1\), and \(M_2\), respectively.
6. It is known that \(D_2 = 380000\) and \(M_2 = 500000\).
7. From the charts it can be deduced: \((1 - 0.35)D_1 = D_2 \rightarrow D_1 = \frac{380000}{0.65} \approx 584615\) and \((1 - 0.1)M_1 = M_2 \rightarrow M_1 = \frac{500000}{0.9} \approx 555555\).
8. The questions asks to find \(D_1 - M_1 = 584615 - 555555 = 29060\), which is about 30000 acres more.
9. Our answer will be: 3.5 and "30000 acres more."
