MATH SOLVE

3 months ago

Q:
# 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?

Accepted Solution

A:

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

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