 WASHINGTON STATE MATHEMATICS COUNCIL 2000 MIDDLE SCHOOL MATH OLYMPIAD   Session II: SIXTH GRADE ALGEBRAIC SENSE 6

1.    When a one-digit number is multiplied by 6, it increases by 20. What is the one-digit number?

2.    There are bicycles and tricycles in the yard. There are a total of 30 seats and 70 wheels. How many tricycles are there?

3.    The total number of spheres (N) needed to make a triangular pyramid is given by the equation

```
N = X3 + X2 +  X
---  ---   ---
6    2     3

```

where X is the number of layers. If I make a triangular pyramid with 8 layers, how many spheres are in the bottom layer?

4.    Twelve people rent a boat. The boat rents for a flat rate, no matter how many people rent the boat. By taking 8 more people, the cost to each person is reduced by \$2.50. How much is the rent for the boat?

Megan is trying to open her combination bicycle lock. The first number was written in the form of a riddle, which read: "2/3 of the number, added to 16, will equal two times as much as the number?  What is the first number in the combination?