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?
Respuestas
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