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# INTERESTING PROBLEMS...

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1) In a school with 600 students, 317 are in the band and 234 are in the orchestra. If 122 students are in neither band nor orchestra, what is the probability that a randomly selected student is only in band or only in orchestra? Express your answer as a common fraction.

2) In shrom currency, 3/7 of a shrim, 4 5/7 shrums, and 14 1/7 shrams have the same value. How many shrums are in one shram and one shrim. Express your answer as a mixed number.

3) It take 50 minutes for 50 machines to make 50 matchbooks. How many minutes will it take for 20 machines to make 20 matchbooks?

Feb 2, 2020
edited by mathleteig  Feb 2, 2020

#1
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1.    If you draw a Venn diagram, you will see 244 in only  band     161 in only orchestra      73 in both   122 neither

out of 600                               244 /600  + 161 /600  = 405/600    =   27 /40

Feb 2, 2020
#2
+22080
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50 mach * 50 min /50 book   = 50 mach-min/ book

50 mach-min / book   / 20 mach       *  20 book    =   50 min

Feb 2, 2020
#3
+22080
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2.

14 1/7 Shram / 4 5/7 Shrum  99/7   *  7/33 = 99/33   =    3 Shram /1 Shrum         so   1 Shram = 1/3 Shrum

4 5/7 shrum  / 3/7 shrim = 33/7 * 7/3 =  33/3 = 11 shrum/shrim         1 shrim = 11 shrum

Feb 3, 2020