word problem-- systems of linear equations

Question

Everyone in the Capulet and Montague families loves 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.

Answer 1

Let's set up the two equations.

 

First let M = Montague and C = Capulet

 

1) Last year      4C + 6M = 100

2) This year      8C +12M = 200

 

The above is your system of equations with two equations and two unknowns (C & M).

 

The problem does not ask to solve this system but rather just set it up, I believe.  If you do try to solve it, you'll find there are multiple solutions.