7 watermelons cost $8.96. Which equation would help determine the cost of 5 watermelons? Choose 1 answer: (A) (x)/(5)=($8.96)/(7) (B) (x)/(5)=(7)/($8.96) (C) (7)/(5)=(x)/($8.96) (D) (5)/(x)=($8.96)/(7) (E) None of the above

Question

7 watermelons cost  $8.96. Which equation would help determine the cost of 5 watermelons? Choose 1 answer: (A)  (x)/(5)=($8.96)/(7) (B)  (x)/(5)=(7)/($8.96) (C)  (7)/(5)=(x)/($8.96) (D)  (5)/(x)=($8.96)/(7) (E) None of the above

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Set Up Proportion: We need to find an equation that relates the cost of 5 watermelons to the cost of 7 watermelons, which is given as $8.96. We assume that the cost per watermelon is constant. Therefore, we can set up a proportion where the cost of 5 watermelons (which we'll call x) is to 5 as $8.96 is to 7.Derive Equation: The correct equation should have the cost of 5 watermelons (x) on one side of the equation and the known cost of 7 watermelons ($8.96) on the other side, with the respective number of watermelons as the other part of the proportion. The equation should look like this: (x/5) = ($8.96/7).Check Options: Now, let's check each option to see which one matches our derived equation: (A) (x/5) = ($8.96/7) - This matches our derived equation. (B) (x/5) = (7/$8.96) - This is incorrect because it suggests that the number of watermelons is inversely proportional to the cost, which is not the case. (C) (7/5) = (x/$8.96) - This is incorrect because it suggests that the ratio of the number of watermelons is equal to the ratio of the cost per watermelon, which is not what we're looking for. (D) (5/x) = ($8.96/7) - This is incorrect because it inverts the relationship between the cost of 5 watermelons and the number 5. (E) None of the above - Since we have found a matching equation in option (A), this is not correct.Identify Correct Equation: Therefore, the correct equation to determine the cost of 5 watermelons is given by option (A): (x/5) = ($8.96/7).

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