A development has 425 new homes for sale.
. . 113 of the homes are green,
. . 315 have a porch,
. . 60 have a garage,
. . 45 are green and have a porch,
. . 23 are green and have a garage,
. . 41 have a porch and a garage,
. . 12 are green and have a have a porch and have a garage.
(a) How many homes are not green, do not have a porch, and do not have a garage?
I tried to put everything into a Venn Diagram to find out where my numbers lie,
then subtracted the total in the circles from the universal set of 425 new homes.
I came up with a total of 34 homes. . Right!
(b) How many homes are not green, but have a porch and a garage?
I looked at how many total homes that have both a garage and a porch,
. . but are not green (241+29) and got 270. . No
I am having problems with the figures to be sure that I accounted for everything correctly:
Green (no porch, no garage) = 57
Green and garage (no porch) = 11
Green and porch (no garage_ = 33
Green, and porch, and garage =12
Garage and porch (not green) = 29 .← This is the answer to (b).
Garage (no porch, not green) = 8
Porch (no garage, not green) = 241
None of these = 34
From this list, I assume your Venn diagram is correct.