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?

Answer:Infinite solutionStep-by-step explanation:Let, number of Capulet family = x and number of Montague family = y.Since, last year, each Capulet wrote 4 essays and each Montague wrote 6 essays.Moreover, total essays wrote last year are 100.So, we get, 4x + 6y = 100.Again, this year, each Capulet wrote 8 essays and each Montague wrote 12 essays.Moreover, total essays wrote this year are 200.So, we get, 8x + 12y = 200.Thus, the system of equations is given by,4x + 6y = 100.8x + 12y = 200.Dividing first equation by 2 and second equation by 4, we get the equation,2x + 3y = 50.Since, there is only one equation and two variables i.e. x and y.There can be infinite number of possibilities for the values of x and y.