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A forest that is populated by crows and doves currently contains a total of 1,500 crow and dove nests. Crows use approximately 8 grams of twigs when building a nest, and doves use approximately 6 grams of twigs when building a nest. Which of the following equations best approximates the relationship between C, the total amount, in grams, of twigs used for crow nests and D, the total amount, in grams, of twigs used for dove nests? Choose 1 answer: (A) (C)/(8)+(D)/(6)=1,500 (B) (C)/(6)+(D)/(8)=1,500 (c) 6C+8D=1,500 (D) 8C+6D=1,500

A forest that is populated by crows and doves currently contains a total of 11,500500 crow and dove nests. Crows use approximately 88 grams of twigs when building a nest, and doves use approximately 66 grams of twigs when building a nest. Which of the following equations best approximates the relationship between C C , the total amount, in grams, of twigs used for crow nests and D D , the total amount, in grams, of twigs used for dove nests?\newlineChoose 11 answer:\newline(A) C8+D6=1,500 \frac{C}{8}+\frac{D}{6}=1,500 \newline(B) C6+D8=1,500 \frac{C}{6}+\frac{D}{8}=1,500 \newline(C) 6C+8D=1,500 6 C+8 D=1,500 \newline(D) 8C+6D=1,500 8 C+6 D=1,500

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Q. A forest that is populated by crows and doves currently contains a total of 11,500500 crow and dove nests. Crows use approximately 88 grams of twigs when building a nest, and doves use approximately 66 grams of twigs when building a nest. Which of the following equations best approximates the relationship between C C , the total amount, in grams, of twigs used for crow nests and D D , the total amount, in grams, of twigs used for dove nests?\newlineChoose 11 answer:\newline(A) C8+D6=1,500 \frac{C}{8}+\frac{D}{6}=1,500 \newline(B) C6+D8=1,500 \frac{C}{6}+\frac{D}{8}=1,500 \newline(C) 6C+8D=1,500 6 C+8 D=1,500 \newline(D) 8C+6D=1,500 8 C+6 D=1,500
  1. Define variables: Let's define the variables:\newlineLet CC be the total amount, in grams, of twigs used for crow nests.\newlineLet DD be the total amount, in grams, of twigs used for dove nests.\newlineLet cc be the number of crow nests.\newlineLet dd be the number of dove nests.\newlineWe know that there are a total of 1,5001,500 crow and dove nests combined, so:\newlinec+d=1,500c + d = 1,500
  2. Total nests and twigs: We also know that crows use approximately 88 grams of twigs per nest, and doves use approximately 66 grams of twigs per nest. Therefore, the total amount of twigs used by crows and doves can be represented as:\newlineC = 8c8c (for crows)\newlineD = 6d6d (for doves)
  3. Expressing twigs in terms of nests: We need to find the relationship between CC and DD. Since we know the number of nests for crows and doves adds up to 1,5001,500, we can express the total amount of twigs used in terms of CC and DD:C+D=total twigs usedC + D = \text{total twigs used}But we need to express CC and DD in terms of the number of nests (cc and dd), so we substitute the expressions for CC and DD from the previous step:8c+6d=total twigs used8c + 6d = \text{total twigs used}
  4. Expressing nests in terms of each other: Now, we need to remember that c+d=1,500c + d = 1,500 (the total number of nests). We can use this information to express dd in terms of cc:\newlined=1,500−cd = 1,500 - c
  5. Analyzing the options: However, we are not asked to solve for the number of nests or the total twigs used. We are asked to choose the equation that best approximates the relationship between CC and DD. Therefore, we do not need to substitute d=1,500−cd = 1,500 - c into the equation 8c+6d=total twigs used8c + 6d = \text{total twigs used}. Instead, we need to look at the options provided and determine which one correctly represents the relationship between CC and DD.
  6. Choosing the correct equation: Let's analyze the options given:\newline(A) C8\frac{C}{8} + D6\frac{D}{6} = 1,5001,500\newlineThis option suggests that the number of crow nests is C8\frac{C}{8} and the number of dove nests is D6\frac{D}{6}, which would mean the total number of nests is 1,5001,500. This seems to align with the information given.\newline(B) C6\frac{C}{6} + D8\frac{D}{8} = 1,5001,500\newlineThis option incorrectly suggests that crows use 66 grams of twigs and doves use D6\frac{D}{6}00 grams of twigs per nest, which contradicts the information given.\newline(C) D6\frac{D}{6}11\newlineThis option incorrectly suggests that the coefficients for D6\frac{D}{6}22 and D6\frac{D}{6}33 should be 66 and D6\frac{D}{6}00, respectively, which does not match the grams per nest for crows and doves.\newline(D) D6\frac{D}{6}66\newlineThis option incorrectly suggests that the total amount of twigs used by crows and doves (in grams) is 1,5001,500, which is not the case; 1,5001,500 is the total number of nests.
  7. Choosing the correct equation: Let's analyze the options given:\newline(A) C8+D6=1,500\frac{C}{8} + \frac{D}{6} = 1,500\newlineThis option suggests that the number of crow nests is C8\frac{C}{8} and the number of dove nests is D6\frac{D}{6}, which would mean the total number of nests is 1,5001,500. This seems to align with the information given.\newline(B) C6+D8=1,500\frac{C}{6} + \frac{D}{8} = 1,500\newlineThis option incorrectly suggests that crows use 66 grams of twigs and doves use 88 grams of twigs per nest, which contradicts the information given.\newline(C) 6C+8D=1,5006C + 8D = 1,500\newlineThis option incorrectly suggests that the coefficients for CC and DD should be 66 and 88, respectively, which does not match the grams per nest for crows and doves.\newline(D) C8\frac{C}{8}22\newlineThis option incorrectly suggests that the total amount of twigs used by crows and doves (in grams) is 1,5001,500, which is not the case; 1,5001,500 is the total number of nests.Based on the analysis, the correct equation that represents the relationship between CC (the total amount, in grams, of twigs used for crow nests) and DD (the total amount, in grams, of twigs used for dove nests) is:\newlineC8+D6=1,500\frac{C}{8} + \frac{D}{6} = 1,500\newlineThis is because C8\frac{C}{8} represents the number of crow nests (since each crow nest uses 88 grams of twigs) and D6\frac{D}{6} represents the number of dove nests (since each dove nest uses 66 grams of twigs). The sum of these two quantities equals the total number of nests, which is 1,5001,500.

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