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The Capulet and Montague families love writing. Last year, each Capulet wrote 4 essays, each Montague wrote 6 essays, and both families wrote 100 essays in total. This year, each Capulet wrote 8 essays, each Montague wrote 12 essays, and both families wrote 200 essays in total. How many Capulets and Montagues are there? Choose 1 answer: (A) There is not enough information to determine the exact number of Capulets and Montagues. (B) The given information describes an impossible situation. (C) There are 16 Capulets and 6 Montagues. (D) There are 6 Capulets and 16 Montagues.

The Capulet and Montague families love writing.\newlineLast year, each Capulet wrote 44 essays, each Montague wrote 66 essays, and both families wrote 100100 essays in total.\newlineThis year, each Capulet wrote 88 essays, each Montague wrote 1212 essays, and both families wrote 200200 essays in total.\newlineHow many Capulets and Montagues are there?\newlineChoose 11 answer:\newline(A) There is not enough information to determine the exact number of Capulets and Montagues.\newline(B) The given information describes an impossible situation.\newline(C) There are 1616 Capulets and 66 Montagues.\newline(D) There are 66 Capulets and 1616 Montagues.

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Q. The Capulet and Montague families love writing.\newlineLast year, each Capulet wrote 44 essays, each Montague wrote 66 essays, and both families wrote 100100 essays in total.\newlineThis year, each Capulet wrote 88 essays, each Montague wrote 1212 essays, and both families wrote 200200 essays in total.\newlineHow many Capulets and Montagues are there?\newlineChoose 11 answer:\newline(A) There is not enough information to determine the exact number of Capulets and Montagues.\newline(B) The given information describes an impossible situation.\newline(C) There are 1616 Capulets and 66 Montagues.\newline(D) There are 66 Capulets and 1616 Montagues.
  1. Equation 11: Let's denote the number of Capulets as CC and the number of Montagues as MM. From the first year's information, we can write the equation:\newline4C+6M=1004C + 6M = 100
  2. Equation 22: From the second year's information, we can write the equation: 8C+12M=2008C + 12M = 200
  3. Comparison: We notice that the second equation is exactly double the first equation. This means that the second equation does not provide new information; it is simply a scaled version of the first equation. Therefore, we cannot solve for CC and MM uniquely with the given information.
  4. Conclusion: Since we cannot determine the exact number of Capulets and Montagues with the given information, the correct answer is (A) There is not enough information to determine the exact number of Capulets and Montagues.

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