An electronics store surveyed every 8th customer who came into the store for a week.

Question

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...)

Answer 1

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.

Answer 2

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!!

Answer 3

Okay so my final answers are:

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