Question

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?

A) There is not enough information to determine
B). The following describes an impossible situation
C). There are 16 capulet and 6 montague
D). There are 6 capulets and 16 montagues

Answer 1

To find the number of Capulets and Montagues, set up a system of equations using the given information, solve the system of equations, and find the values of x and y. There are 6 Capulets and 16 Montagues.

Step-by-step explanation:

To solve this problem, we can set up a system of equations using the given information. Let's assume that there are x Capulets and y Montagues.

From the information given last year, we know that each Capulet wrote 4 essays and each Montague wrote 6 essays, and the total number of essays written by both families was 100.

This can be represented by the equation 4x + 6y = 100.

Using the information given this year, we know that each Capulet wrote 8 essays and each Montague wrote 12 essays, and the total number of essays written by both families was 200.

This can be represented by the equation 8x + 12y = 200.

Now we can solve this system of equations to find the values of x and y.

By solving these equations, we find that x = 6 and y = 16.

Therefore, there are 6 Capulets and 16 Montagues.