2A) 8N = (64/8)N = 64*(N/8) = 64*(.25)
8N = 16
2B) S:N:J = 5:3:1
S - N = 5 - 3 = 2 "ratio units" = 16 games. Jay has 1 "ratio unit" of games.
Jay has 8 games.
2C) The upper left box must be 6, so the boxes on the right must be 2, 3, 4 in some order. The top box cannot be 2 or 3 because those choices cause a number to be used twice. The top right box is 4, the middle right box is then 3, and the bottom box must be ...
A = 2.
2D) 4 half-squares are unshaded for a total of 2 of the 9 squares. Then the 7 shaded squares are 14 cm², or 2 cm² per small square. The 9 small squares add to ...
18 cm²
2E) The Nth triangular number is the sum of all positive integers N and below. That is, the 4th triangular number is 4 + 3 + 2 + 1 = 10. The 5th triangular number adds 5 to that sum, so is 15. The Nth triangular number is the number of handshakes there will be between N+1 people.
If there are 15 handshakes, there are 6 people in the room.
(The Nth triangular number t(n) is given by t(n)=n(n+1)/2. This can give rise to a quadratic equation that you can solve to find the number of people.)
