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?

Answer 1

Respuesta:

x= 10, y=10

Explicación paso a paso:

Hi.

For this problem, the number of members of the Capulet family will be represented by "x" and the number of family members  of the Montague family by "y".

Then:

"each Capulet wrote 4 essays, each Montague wrote 6 essays, and both families wrote 100 essays in total."

4x+6y=100  (eq.1)

and:

"each Capulet wrote 8 essays, each Montague wrote 12 essays, and both families wrote 200 essays in total."

8x+12y=200 (eq.2)

Now, I will clear x, of eq.1

4x+6y=100

4x=100-6y

x= (100-6y)/4

x= 25- 1.5y  (eq.3)

And now, I will replace this value in the eq.2

8(25- 1.5y)+12y=200

200- 12y+12y=200

0=0

This equation does not allow to know the value of x. But Now we know that it's a system with infinite solutions. Only whit this info, we can't know which is the number of family member. However, if we graph these equations, we will find 2 possible cases that solve the problem, because we cannot say that the family has 0.1 members, the acceptable values are:

x= 10, y=10

x=25, y=0

and the most acceptable values are:

x= 10, y=10