Question

1. the venn diagram below shows

the number of 8th grade students
who have a smartphone or tablet.
smartphone
116
58
tablet
29
117
a. how many students have a smartphone and a tablet?

b. how many students do not have a smartphone or tablet?

c. how many 8th grade students are there?

d. how many students have a tablet?

e. how many students have a smartphone but not a tablet?

Explanation:

Step1: Find overlap (both devices)

The overlapping section of the Venn diagram is the number of students with both a smartphone and a tablet: $58$

Step2: Find students with neither device

The number outside both circles is students with neither: $117$

Step3: Calculate total students

Sum all sections of the Venn diagram: $116 + 58 + 29 + 117$

$$\begin{align*} 116 + 58 &= 174 \\ 174 + 29 &= 203 \\ 203 + 117 &= 320 \end{align*}$$

Step4: Find total with tablet

Sum tablet-only and overlap: $29 + 58 = 87$

Step5: Find smartphone only

Use smartphone circle minus overlap: $116$

Step6: Calculate total with smartphone or tablet

Subtract neither from total students: $320 - 117 = 203$

Answer:

a. 58
b. 203
c. 320
d. 87
e. 116