Question

The Capulet and Montague families love writing. Last year, each Capulet wrote 44 essays, each Montague wrote 66 essays, and both families wrote 100100 essays in total. This year, each Capulet wrote 88 essays, each Montague wrote 1212 essays, and both families wrote 200200 essays in total. How many Capulets and Montagues are there?

Answer 1

Answer: The answer is 2275 and 0.

Step-by-step explanation:  Given that the Capulet and Montague families love to write. Last year, each Capulet wrote 44 essays, each Montague wrote 66 essays and both families wrote 100100 essays in total. This year, each Capulet wrote 88 essays, each Montague wrote 1212 essays, and both families wrote 200200 essays in total. We are to find the number of Capulets members and Montagues members.

Let there are 'x' members in Capulet family and 'y' members in the Montague family. Then, we have

$44x+66y=100100,\\\\88x+1212y=200200.$

Multiplying first equation by 2 and then subtracting from the second equation, we have

$1212y-132y=200200-200200\\\\\Rightarrow 1080y=0\\\\\Rightarrow y=0.$

So,

$x=\dfrac{100100}{44}=2275.$

Thus, there are 2275 Capulets and 0 Montagues.