Question

When Cedric walked into a party, two-thirds of those invited had already arrived. Six more people arrived just after Cedric, bringing the number at the party to $\frac{5}{6}$ of those invited. What was the total number of invited guests?

Answer 1

42 People

Explanation:

P is the total amount of people. Before Cedric arrived, there were (2/3)P people at the party. After Cedric and six other people arrived, there are (2/3)P+7 people at the party. Since this is the same as (5/6)P, we solve (2/3)P+7=(5/6)P to find that P=42.

Answer 2

Answer: Hence, there are 36 total number of invited guests.

Explanation:

Let the total number of invited guests be 'x'

Part of those invited had already arrived =
`(2)/(3)x`

Number of people just arrived = 6

According to question, it brings the number at the party to
`(5)/(6)` of those invited.

So, it becomes,

`(2)/(3)x+6=(5)/(6)x\\\\6=(5)/(6)x-(2)/(3)x\\\\6=(5x-4x)/(6)\\\\6=(x)/(6)\\\\x=6* 6\\\\x=36`

Hence, there are 36 total number of invited guests.