3 1/2 times as many guests arrived as expected. If 105 guests were unexpected, how many guests were expected?

42.

Let e = expected guests and u = unexpected guests.

3.5e = u + e (we are told the total number of guests is 3.5 times the expected)

We are also told the unexpected (u) numbered 105. Substituting 105 for u, the equation becomes:

3.5e = 105 + e, or

2.5e = 105, or

e= 42

So, they expected 42 and another 105 unexpected arrived, for a total of 147 guests.

30

30

x guests were expected.

3.5x guests arrived

Of these 3.5x, since x were expected, then 3.5x - x = 2.5x were unexpected. So 2.5x = 105

a few

3.5x=105

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3.5/105 = x

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30=x