Question

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

Answer 1

Using two equations derived from the information provided for last year and this year (4C + 6M = 100 and 8C + 12M = 200), we find that after simplification both years have consistent conditions. The only option that maintains the ratio and satisfies the conditions is 6 Capulets and 16 Montagues.

Step-by-step explanation:

Let us denote the number of Capulets by C and the number of Montagues by M.

Information from Last Year:

4C + 6M = 100 (Each Capulet wrote 4 essays and each Montague wrote 6, resulting in a total of 100 essays.)

Information from This Year:

8C + 12M = 200 (This year, each Capulet wrote 8 essays and each Montague wrote 12, resulting in a total of 200 essays.)

The second equation can be simplified by dividing the entire equation by 2, which would give us the first equation: 4C + 6M = 100. Since both years produce the same equation after simplification, it means that the conditions are consistent and the numbers of Capulets and Montagues multiplied by their respective number of essays both years have a proportional relationship.

Therefore, the answer must maintain the ratio from last year. Hence, by looking at the options provided, only option D, which is 6 Capulets and 16 Montagues, maintains the ratio such that (4*6) + (6*16) equals 100 essays from last year and (8*6) + (12*16) equals 200 essays from this year.

The correct answer is D: There are 6 Capulets and 16 Montagues.