9514 1404 393
Answer:
0 people ate dinner
23 people ate lunch
Step-by-step explanation:
If the bill is split evenly between x people, then each pays 500/x.
Splitting the bill between x-1 people means each pays 500/(x -1).
When the difference in those amounts is 1.00, we have ...
500/(x -1) -500/x = 1
500 = x(x -1)
Completing the square gives ...
500.25 = (x -0.5)²
x = 0.5 +√500.25 ≈ 22.866 ≈ 23
Check
With 22 people splitting the $500 bill, the amount each pays is ...
$500/22 ≈ $22.73
With 23 people splitting the bill, the amount each pays is ...
$500/23 ≈ $21.74
The difference is $0.99, about $1.00. This is as close as you will get with these numbers.
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23 people at lunch, including Stewart.
