Each month, a new set of puzzles will be posted.  Come back next month for the solutions and a new set of puzzles, or subscribe to have them sent directly to you.

 There are 10 points equally spaced around the circle with interconnecting lines drawn between them. How many lines are needed to draw the 10 point pattern shown below? How many lines would you need for 50 points on the circle? How many lines would you need for 100 points on the circle? In 2015 the populations of City X and City Y were equal. From 2010 to 2015, the population of City X increased by 20% and the population of City Y decreased by 10%. If the population of City X was 120,000 in 2010, what was the population of City Y in 2010?   Two bicycles start at the intersection of two perpendicular roads. One rides west at a rate of 9 miles per hour, while the other rides south at a rate of 12 miles per hour. If both traveled in the same plane, how many miles are they in the shortest distance between them at the end of 3 hours?   The amount of money a performer earns is directly proportional to the number of people attending the performance. The performer earns £60 a performance for every 12 people attending. The performer pays 43% of the money earned to pay the organizer’s costs in putting on each performance. The rest of the money earned is the performer’s profit. What is the profit that the performer makes at a performance where 48 people attend? If the organizer receives £7.50 per person, per performance, what is the profit that the organizer make per performance?

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##### Last month's solutions
 Point P is the center of the circle in the figure below. What is the value of angle BPC or xº?. Solution: By joining the points A and P with line AP, triangles ABP and ACP are isosceles because lines AP = PB = PC and angles PAB = PAC and ABP = ACP. Therefore, angles APB and APC = 180º – 20º – 20º = 140º and xº = 360º – 140º – 140º = 80º. An online bookstore sells novels and magazines. Each novel sells for \$4, and each magazine sells for \$1. If Fiona purchased a total of 11 novels and magazines that have a combined selling price of \$20, how many novels did she purchase? Solution: Let x = total number of novels and y = total number of magazines. x + y = 11, y = 11 – x 4x + 1y = 20, 4x + (11 – x) = 20 3x + 11 = 20 or 33x = 9 and therefore x = 3 novels The mean score of 8 players in a basketball game was 14.5 points. If the highest individual score is removed, the mean score of the remaining 7 players becomes 12 points. What was the highest score? Solution: Let x = total score for 8 players and y = total score for 7 players. x = 14.5 points * 8 players = 116 points and y = 12 points * 7 players = 84 points The highest score that was removed = x – y = 116 – 84 = 32 To check: 84 (7 players) + 32 (1 player) = 116 and 116 / 8 = 14.5 pints (mean score for 8 players).