Use the following information to determine the number of people in each region of the Venn Diagram

174 people were asked which of these instruments that they could play: Piano, Drums, or Guitar.
33 people could play none of these instruments.
9 people could play all three of these instruments.
43 people could play drums or guitar but could not play piano.
71 people could play guitar.
96 people could play at least two of these instruments.
50 people could play piano and guitar but could not play drums.
39 people could play piano and drums.
Guitar Piano Drums

Nah they did my mans dirty

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To determine the number of people in each region of the Venn Diagram, we will need to go step by step, using the given information:

1. Start with the total number of people surveyed: 174.

2. Subtract the number of people who cannot play any of the instruments: 33.
Total now: 174 - 33 = 141.

3. Subtract the number of people who can play all three instruments: 9.
Total now: 141 - 9 = 132.

4. Subtract the number of people who can play drums or guitar but not piano: 43.
Total now: 132 - 43 = 89.

5. Subtract the number of people who can play guitar: 71.
Total now: 89 - 71 = 18.

6. Subtract the number of people who can play at least two instruments (excluding those who can play all three): 96.
Total now: 18 - 96 = -78.

Since we have a negative value, it means there is a contradiction or error in the given information. Please verify the data and make sure all the numbers are accurate and consistent.

To determine the number of people in each region of the Venn diagram, we'll go step by step by using the given information.

Let's denote the number of people who can play the piano as P, the number of people who can play the drums as D, and the number of people who can play the guitar as G.

First, we know that 174 people were asked about their instrument skills, and 33 of them could play none of these instruments. This means that the total number of people who can play at least one of these instruments is 174 - 33 = 141.

Next, we are given that 9 people can play all three instruments. Since these 9 people are counted in the "at least one" category, we need to subtract them once from each instrument's count. So we have:
P + D + G = 141 - 9 = 132 (Equation 1)

We are also given that 43 people can play either the drums or the guitar but not the piano, and 71 people can play the guitar. Since the total number of people who can play the guitar includes both those who can play only the guitar and those who can play the guitar along with other instruments, we need to subtract the number of people who can only play the guitar from the total number of people who can play the guitar. Let's denote the number of people who can only play the guitar as G1. So we have:
(G - 9) + (D - 43) + G1 = 71 (Equation 2)

Furthermore, we know that 96 people can play at least two of these instruments. This includes those who can play all three instruments. So we subtract the 9 people who can play all three from 96, and denote the remaining count as X. So we have:
X + 9 = 96 => X = 96 - 9 = 87

Now, let's look at the overlaps between pairs of instruments:

- 50 people can play both the piano and the guitar but not the drums.
Let's denote the number of people who can play both the piano and the guitar as P1. So we have:
P1 + 9(P - 50) = 87 (since X represents people who can play at least two instruments, and P - 50 can play only piano and guitar)

- 39 people can play both the piano and the drums.
Let's denote the number of people who can play both the piano and the drums as P2. So we have:
P2 + 9(D - 39) = 87 (since X represents people who can play at least two instruments, and D - 39 can play only piano and drums)

Now we can calculate the values of P, D, and G.

Using Equation 1, we can substitute the values of D and G in terms of P:
P + D + G = 132
P + (P2 + 9) + (P1 + 9 + 50) = 132
3P + P1 + P2 + 68 = 132
3P + P1 + P2 = 132 - 68
3P + P1 + P2 = 64 (Equation 3)

Using Equation 2, we can substitute the values of D - 43 and G - 9 in terms of G1:
(G - 9) + (D - 43) + G1 = 71
(G - 9) + (G1 + 43 - 43) + G1 = 71
2G + G1 - 9 = 71
2G + G1 = 71 + 9
2G + G1 = 80 (Equation 4)

Using Equation 3 and Equation 4, we have a system of two equations with two unknowns (P, P1, P2, G, and G1):
3P + P1 + P2 = 64 (Equation 3)
2G + G1 = 80 (Equation 4)

Solving this system of equations will give us the values of P, P1, P2, G, and G1, which will allow us to determine the number of people in each region of the Venn diagram.