Stewart goes out for lunch with some of his friends. The total bill comes to $500. The friends think that since it is Stewart’s birthday, he shouldn't have to pay. They split the cost of his lunch, with each friend paying an additional
$1
a) How many people ate dinner? Including Stewart

9514 1404 393

  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.

__

23 people at lunch, including Stewart.

36 girls

step-by-step explanation:

the 48 boys is 4 parts of the ratio

divide 48 by 4 to obtain one part of the ratio

= 12 ← 1 part of the ratio

3 parts = 3 × 12 = 36 ← number of girls