A survey asked buyers whether color, size, or brand influenced their choice of cell phone. The
results are below.
185 said size.
147 said brand.
206 said color.
99 said size and brand.
111 said color and size.
52 said color and brand.
39 said all three.
76 said none of these
How many buyers were influenced by color and size, but not brand?
How many buyers were not influenced by color?
How many buyers were surveyed?
Question Help. EMessage instructer

To find how many buyers were influenced by color and size but not brand, we first determine the number of individuals influenced by all three factors. Since 39 people were influenced by all three categories, we can use this to solve our problem. The number influenced by color and size is given as 111. To find those influenced by color and size but not brand, we subtract those influenced by all three from that total: 111 - 39 = 72. So, 72 buyers were influenced by color and size but not brand.

Next, to determine how many buyers were not influenced by color, we first find the total number of influenced buyers. The individual totals for color, size, and brand, accounting for overlaps and those with no influence, can be summed like this:

Total influenced = . So, 467 buyers were surveyed in total.

To find those not influenced by color, consider that 206 people were influenced by color. Thus, the number of buyers not influenced by color can be calculated as follows: Total buyers surveyed - those influenced by color = 467 - 206 = 261. So, 261 buyers were not influenced by color.