In a group of 32 musicians, all play piano, guitar, or both. Of those musicians, 12 only play guitar, and 16 play both. How many of the musicians play only piano? (1 point)

Question

4
8
16
20

Answer 1

There are different methods to approach this problem, but one possible way is to use a Venn diagram. Draw two circles to represent the groups of musicians who play piano (P) and guitar (G), and let the overlap represent those who play both (B). Label the regions outside the overlap P-only and G-only, as well as the given values:

12 musicians only play guitar, so put this number in the G-only region:

```
G: 12

/\
/ \
----

P-only B G-only
```

16 musicians play both piano and guitar, so put this number in the overlap:

```
G: 12
----
/ \
/ \
/--------\
| B |
\--------/
\ /
\ /
\/
P-only B G-only
```

We want to find how many musicians play only piano, which is the number in the P-only region. To get this value, we need to use the fact that "all play piano, guitar, or both", which means that the total number of musicians must be the sum of those in each region:

```
G: 12 Total: 32
----
/ \
/ \
/--------\
| B |
\--------/
\ /
\ /
\/
P-only B G-only
```

We can set up an equation based on this information:

```
P-only + B + G-only = Total
P-only + 16 + 12 = 32
P-only = 4
```

Therefore, there are 4 musicians who play only piano. The answer is 4.