1. A geometric progression is a sequence of numbers with the property that any two consecutive numbers have the same ratio. If x, 3x + 1, and 6x + 2 are in a geometric progression, what could x be?

2. Which pairs of numbers (x,y) satisfy both x + y = 2 and x + y^2 = 4?

3. Van ordered a gross of $18.00 sunglasses for his store. He marked them up 50% when he sold them. After 9 weeks, he put them on sale for 75% off the selling price. Nolan sold 2/3 of his sunglasses at the regular price and 1/3 at the sale price. Did Van make a profit on this shipment of sunglasses? If so, how much?

6. Jack has moles digging tunnels all over his backyard. The exterminator told him he would have to place a mole trap every 10 feet along the main mole burrow. The mole burrow runs diagonally through Jack's rectangular backyard, which measures 50 feet * 75 feet. How many mole traps will he need?

4. Gavin spends 7.25 hours in class each day, Monday through Friday. He is creating a pie chart to visually display the amount of time he spends in class in a 7-day week to compare with his other weekly activities. Find the angle measure of the sector of the pie chart that represents the amount of time he spends in class in 1 week.

5. The first three terms of a particular arithmetic sequence are 1/2, 1, and 3/2. Change one of these first three terms to create the first three terms of a geometric sequence. Find the three different solutions.