Hello, tizpan!

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.