Question

Alyssa, bert, and cara are running for school president. alyssa receives one-third of the votes. bert receives 60 percent of the remaining votes, and the rest of the votes go to cara. if cara receives 96 votes, how many votes were there in all?

Answer 1

Let x be the total amount of votes. So
Alyssa receives a third of the votes
A=x/3

Very receives 60 percent of what's left. Since Alyssa receives one third of the votes. That means that two thirds of the votes remain. So 60 percent of 2/3 of the votes go to Bert
B=0.6 * (2x)/3

If the rest of the votes go to Cara that means she has to revive 40% of the votes that Alyssa got (because Bert got 60)

And we know how many votes she got, 96.
So 96 is equal to 0.4 * (2x)/3

Simply to (96 * 3)/(0.4 * 2) = x

Answer 2

See answer below......