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MathMagic Cycle 3 Problems - GOOD LUCK!
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***** 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?
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***** 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?
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