Question

the capulet and montague families love writing. last year, each capulet wrote 4 44 essays, each montague wrote 6 66 essays, and both families wrote 100 100100 essays in total. this year, each capulet wrote 8 88 essays, each montague wrote 12 1212 essays, and both families wrote 200 200200 essays in total. how many capulets and montagues are there?

Answer 1

There are 5000 Capulets and 2200 Montagues.

Step-by-step explanation:

We can solve this problem using a system of linear equations. Let's represent the number of Capulets as 'C' and the number of Montagues as 'M'. From the information given, we can set up two equations:

4.44C + 6.66M = 100100 (equation 1)

8.88C + 12.12M = 200200 (equation 2)

We can then solve this system of equations using substitution or elimination. Let's use elimination to eliminate the decimals from equation 1:

1. Multiply equation 1 by 100 to get rid of the decimals. We get 444C + 666M = 10010000 (equation 3)
2. Multiply equation 2 by 45 to make the coefficients of 'C' the same. We get 399C + 545.4M = 9018000 (equation 4)
3. Subtract equation 4 from equation 3 to eliminate 'C'. We get 45M = 99000
4. Divide both sides by 45 to solve for 'M'. We get M = 2200
5. Substitute the value of 'M' into either equation to solve for 'C'. Using equation 1, we get 4.44C + 6.66(2200) = 100100
6. Simplify the equation and solve for 'C'. We get C = 5000

Therefore, there are 5000 Capulets and 2200 Montagues.