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A debt of $450 is to be shared equally among the members of the Outing Club. When five of the members refuse to pay, the other members’ shares each go up by $3. How many members does the Outing Club have?

Respuesta :

x = The number of members 

450 / x = Each person's share 

(450 / x) + 3 = Having gone up by three dollars 

(450 / (x - 5)) = Each person's share minus the five deadbeats 

(450 / x) + 3 = 450 / (x - 5) 

Solve for x... 

450 + 3x = 450x / (x - 5) 

450(x - 5) + 3x(x - 5) = 450x 

450x - 2250 + 3x² - 15x - 450x = 0 

3x² - 15x - 2250 = 0 

3(x - 30)(x + 25) = 0 

x = 30, -25 

The negative result is meaningless... 

x = 30 members
fichoh

The Number of members in the outing club obtained using factorization is 30

Debt amount = 450

Let total number of members = x

Amount to be paid shared equally = 450/x

When 5 members refuse to pay :

  • Amount paid per person = (450/x) + 3

Amount paid per person excluding the 5 members :

  • (450/x-5)

Hence,

(450/x)+3 = (450/x-5)

450+3x = 450 / (x - 5)

450(x - 5) + 3x(x - 5) = 450x

450x - 2250 + 3x² - 15x = 450x

3x² + 2250 - 15x = 0

x² - 5x + 750 = 0

x² - 30x + 25x + 750 = 0

x(x - 30) +25(x - 30) = 0

x = 30 or x = - 25

x cannot be negative ;

Therefore, x = 30 ; number of members in the club ls 30

Learn more : https://brainly.com/question/18796573

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