Question

Upon examining the contents of 38 backpacks, it was found that 23 contained a black pen, 27 contained a blue pen, and 21 contained a pencil, 15 contained both a black pen and a blue pen, 12 contained both a black pen and a pencil, 18 contained both a blue pen and a pencil, and 10 contained all three items. How many backpacks contained none of the three writing instruments?

Answer 1

let n be the total backpacks

so n = 38

23 backpacks contained black
27 contained blue
21 contained pencil

15 containe both black and blue
12 contained black and pencil
18 contained blue and pencil

10 contained all three

agree with that list?

Answer 2

yes

Answer 3

now... draw the venn diagram

Answer 4

it says 10 contained all three

Answer 5

ok

Answer 6

so... if the middle is 10... what do you think is this value?

Answer 7

hint: black and pencil is 12

Answer 8

2

Answer 9

right

then what would be the value of *only* black if the total black is 23?

Answer 10

i'm not sure still

Answer 11

6

Answer 12

hmm... i forgot...you need to solve for the intersection of black and blue first...
so what would be the value of that if black and blue is 15?

Answer 13

5

Answer 14

yes 6 is right for only black

Answer 15

now solve for this