sets, maths

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A survey of 500 television viewers produced the following information,285 watch football,195 watch hockey,115 watch basketball,45 watch football and
basketball,70 watch football and hockey,50 watch hockey and basketball and 50 do not watch any of the three games.
1)How many watch all the three games?
2)How many watch exactly one of the three games?

reply fast! tmr is my maths test.

  • sets, maths -

    I assume you did this with Venn diagrams

    We don't know how many watch all three, label that x
    look at the intersection of the hockey and Football circles, it says 70 watch both
    but we already have x accounted for, so place 70-x in the part showing only hockey and football
    insert 45-x and 50-x in the other overlaps in the same way.
    Now look at the hockey circle
    We already have entries of x, 70-x, and 50-x
    so the part showing ONLY hockey = 195 - x - (70-x) - (50-x)
    = 75+x
    repeat for the other two circles

    now add them all up and set equal to 500
    solve for x (it better be a whole positive number)

    now you can fill in all the values, and all mysteries will be revealed.

  • good grief !!! - sets, maths -

    Just realized looking at the Related Questions below, that I answered this same question for you back in July of this year.

    What gives ????

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