Elmhurst elementary organized an ice cream social for the incoming sixth graders. At the social, 7 students chose vanilla ice cream for every 5 that chose chocolate ice cream. If 84 students chose vanilla ice cream, how many students chose chocolate ice cream?

For this problem I recommend using the explicit version of the arithmetic sequence formula
an = a1 + (n – 1)d.

The first term is a1, the common difference is d, and the number of terms is n. an is the final number we are looking for.

We shall substitute in the common difference and 2 since every hour 2 more people will know. Also the first term is equal to 2. an is 450 because that's what we are looking for.

the equation looks like 450= 2 + (n – 1)2. Now we evaluate. n = 225. 225 terms will pass, then all 450 students will know the rumor. Each term will equal 1 hour . 225 hours converts to 9 full days and 9 hours. So it will take 9 days and 9 hours for every student to know the rumor at that rate.