Out of 384 guests at a conference quarter took their coffee with sugar only 58 it both milk and one out every 16 the rest it?

According to the given information:

- A quarter of the guests (T/4) took their coffee with sugar only.

- 58 guests took it with both milk and sugar.

- One out of every 16 guests (T/16) took it without sugar or milk.

We can calculate the number of guests who took their coffee without sugar or milk as follows:

Guests without sugar or milk = T/16

Now, let's find the total number of guests who took their coffee with sugar (either only sugar or with both milk and sugar):

Guests with sugar = (T/4) + 58

To find the total number of guests, we need to add the number of guests who took their coffee with sugar and the number of guests who took it without sugar or milk:

T = (T/4) + 58 + (T/16)

To clear the fractions, we can multiply both sides by the LCM of 4, 16, and 1, which is 16:

16T = 4T + 768 + T

Combining like terms, we have:

16T - 4T - T = 768

11T = 768

Now, we can solve for T by dividing both sides by 11:

T = 768/11

T = 70

Therefore, the total number of guests at the conference is 70.