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

Answer:

42 People

Step-by-step 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.

Step-by-step explanation:

Let the total number of invited guests be 'x'

Part of those invited had already arrived = $\dfrac{2}{3}x$

Number of people just arrived = 6

According to question, it brings the number at the party to $\dfrac{5}{6}$ of those invited.

So, it becomes,

$\dfrac{2}{3}x+6=\dfrac{5}{6}x\\\\6=\dfrac{5}{6}x-\dfrac{2}{3}x\\\\6=\dfrac{5x-4x}{6}\\\\6=\dfrac{x}{6}\\\\x=6\times 6\\\\x=36$

Hence, there are 36 total number of invited guests.