Roslyn has ten boxes. Five of the boxes contain pencils, four of the boxes contain pens, and two of the boxes contain both pens and pencils. How many boxes contain neither pens nor pencils?
I need to find out how many boxes have no writing utensils at all. I can use a Venn diagram to represent the situation. I draw two overlapping circles, one for pens and one for pencils, and a rectangle around them to represent the ten boxes. I know that two boxes have both pens and pencils, so I write 2 in the intersection of the circles. I also know that four boxes have pens, so the rest of the pen circle must have 4 - 2 = 2 boxes that have only pens. I write 2 in that region. Similarly, five boxes have pencils, so the rest of the pencil circle must have 5 - 2 = 3 boxes that have only pencils. I write 3 in that region. Now I have accounted for 2 + 2 + 3 = 7 boxes. The remaining 10 - 7 = 3 boxes must be outside the circles, meaning they have neither pens nor pencils. I write 3 in the rectangle outside the circles. Therefore, the answer is 3. 