Question

A group of students planned to chip in to raise a total of $100 for one of their friends’ birthday party but 5 persons couldn’t come so they didn’t pay. This increased the share of the others by $1 each. Find the amount that each person paid after

Answer 1

$5

Explanation:

Let the number of students be x, then

Initial amount per student was:

• 100/x

After it becomes:

• 100/(x - 5)

Since amount increased after, it can be shown as:

• 100/x + 1 = 100/(x - 5)

Multiply each term by x(x - 5) to get rid of the fraction:

• 100(x-5) + x(x - 5) = 100x
• 100x - 500 + x² - 5x - 100x = 0
• x² - 5x - 500 = 0

Positive solution of this quadratic equation is

• x = 25

Amount each person paid after:

• $100 / (25 - 5) = $5