Respuesta :
Answer:
1 member played both instruments.
Step-by-step explanation:
Lets call:
A: the number of people that only play the piano
B: the number of people that played both
C: the number of people that only play the guitar
D: the number of people that didn't play either of these two instruments.
If the music club has 23 members, we can write the following equation:
A + B + C + D = 23 (Equation 1)
At the same way, from the sentences 10 people played the piano, 9 people played the guitar, and 5 people didn't play either of these two instruments, we can write the following equations:
A + B = 10 (Equation 2)
B + C = 9 (Equation 3)
D = 5 (Equation 4)
So, replacing equation 2 and 4 on equation 1 and solving for C, we get:
(A+B) + C + D = 23
10 + C + 5 = 23
C + 15 = 23
C = 23 - 15
C = 8
Then, replacing the value of C on equation 2 and solving for B, we get:
B + C = 9
B + 8 = 9
B = 9 - 8
B = 1
Finally the number of club members that played both the piano and the guitar is 1 person.
