Hello,
I have a question concerning the difference between Number 105 and 113 in PS, OG 13. In general, both tasks can be solved by using the unknwon multiplier, which i thought to be comfortbale with.
105 is absolutely obvios to me: I set up the equation: (30x+50)/(x+5)=25/1. This results in x=15. Because of the X beeing 1, concerning the teachers i get 1x15=15.
So the present number of teachers is 15.
I apllied the same logic for 113: I set up the equation: (3x+600)/(5x+500)=4/5. This yields x=200. For the present number of Republicans i get 3x200=600 and for Democrats i get 5x200=1000. Thus the difference should be, according to the same logic as in 105, 400 and not 300.
The video solution of MGMAT adds the new registered voters, before subtracting. 600 for the Reps and 500 for the Democrats. This yields: (1000+500)-(600+600)=300.
I do not understand why the 500 and 600 in 113 have to be added after getting the unknown multiplier. If this is true, why arent we forced to do the same in 105? We would have to add the increase of teachers of 5 and this would yield 15+5=20.
I am totally confused because of the different solutions, although both tasks seem similar to me.
Thanks for your support
Sebastian