------------------------------------------------- MathMagic Cycle 3 Problems - GOOD LUCK! -------------------------------------------------- ***** MathMagic Problem Cycle 3: Level 7-9 Regular ***** As you know, a cassette tape has two sides, side A and side B. Several songs and their lengths in minutes and seconds are listed below. Your job is to schedule the songs in the most efficient manner. In making your decisions, remember it is desirable to arrange the songs on both sides so that as little tape as possible is used and so that the total lengths of play time on the two sides are as even as possible. Song 1: 2:30 minutes Song 2: 1:50 minutes Song 3: 4:25 minutes Song 4: 3:23 minutes Song 5: 2:48 minutes Song 6: 3:00 minutes Song 7: 2:27 minutes Song 8: 3:27 minutes Song 9: 4:10 minutes In forming your solution, answer these questions: 1) What is the total length of the music in minutes and seconds? 2) What songs are on side A and what songs ar on side B to minimize the amount of tape needed? 3) What is the difference in the amount of time music plays on each side of your arrangement? 4) What is the length of time one side will play from beginning to end if the songs are separated by 3 seconds of silence? --------------------------------------------------------------------- ***** MathMagic Problem Cycle 3: Level 7-9 Advanced ***** A diophantine equation is an equation in which only integer solutions are desired. Example: a solution to 3x + 4y = 11 is x= 1 and y = 2 since 3(1) + 4(2) = 11 1) Find TWO sets of solutions to the diophantine equations and explain your solution strategy. a) 5x + 4y = 32 b) 6x + 4y = 18 2) A school ordered books and calculators. The books cost \$8 each and the calculators cost \$10 each. a) Write an equation which can be used to represent the cost of the books and calculators is \$74 was spent. b) How many books and how many calculators could the school have purchased? ----------------------------------------------------------------------