Math-Can u help me Reiny?

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An electronics store surveyed every 8th customer who came into the store for a week.
Of the 380 people who responded,

185 people watched movies on VHS tapes.
251 people watched movies on DVDs.
72 people watched movies both on VHS tapes and DVDs.

i. Of those surveyed, how many watched only VHS tapes?
ii. Of those surveyed, how many watched only DVDs?
iii. Of those surveyed, how many watched VHS tapes or DVDs, but not both?
iv. Of those surveyed, how many watched VHS tapes or DVDs, or both?

(I'm not sure how if this is a trick question or what, please help...)

  • Math-Can u help me Reiny? -

    make a Venn diagram of two intersecting circles, call one V for VHS, the other D for DVD

    put 72 in the intersection of the two circles

    Now 185 will go into circle V, but you already have 72 of those in the intersection , so put 113 in V outside the intersection.
    You have 251 to go into circle D, but D alreasdy contains 72 of those, so that leaves 179 for the open part of D

    Add them up: 113+72+179 = 364
    but 380 were surveyed, which means that 16 must not watch either VHS or DVD

    put a rectangle around the two circles and place 16 inside the rectangle but outside the circles.

    You should be able to answer any of your questions from the diagram.

  • Math-Can u help me Reiny? -

    GREAT!!! I understand it now....its weird though because I got the same answer 364, but I just added 185+251=436-72=364 and then subtracted 364 from 380 and got 16 remaining....haha THANKS SO MUCH!!

  • Math-Can u help me Reiny? -

    Okay so my final answers are:

    i. 113
    ii. 179
    iii. 292 (add 113+179)
    iv. ?? i think its 72 ??

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