Ask Question
21 July, 01:38

In a music club with 23 members, 10 people played the piano, 9 people played the guitar, and 5 people didn't play either of these two instruments. How many club members played both the piano and the guitar?

+2
Answers (1)
  1. 21 July, 02:00
    0
    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.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “In a music club with 23 members, 10 people played the piano, 9 people played the guitar, and 5 people didn't play either of these two ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers