WASHINGTON STATE MATHEMATICS COUNCIL 1999 MIDDLE SCHOOL MATH OLYMPIAD SEVENTH GRADE ALGEBRAIC SENSE Make sure you include proper units in your answer! 7

1. A girl asked her father how old she is. Her father said that the girl is 1/3 of his age, and that in 15 years she would be 1/2 of his age. How old is the girl?

2. A box contains marbles in four colors: blue, green, red, and yellow. On a balance scale:

• one blue marble balances 3 green marbles and 2 red marbles
• two green marbles balance 4 red marbles and 2 yellow marbles
• four red marbles balance 5 yellow marbles.

How many yellow marbles balance one blue marble?

3. A gray squirrel has 65 nuts gathered in its nest, and a red squirrel has 114 nuts gathered in its nest. A wily woodpecker steals nuts from both squirrels' nests. It steals 2/3 as many nuts from the nest of the gray squirrel as it steals from the nest of the red squirrel. After the woodpecker takes the nuts from both nests, the red squirrel has twice as many nuts left as the gray squirrel has. How many nuts does the gray squirrel have left?

 4 How many intersections of two or three line segments are there on the surface of the cube at right? [Note: The cube is a 4-inch cube. The segments are all spaced 1 inch apart.]

 5 How many dots would there be in the tenth figure in the sequence at right?