Question

An excursion party had $2.00 to pay in total, but before the bill was paid 10 people from the party went away, and those that remained had each to pay 10 cents more. Write an equation that can be used to find how many were in the party at first?

Answer 1

Answer:

20 people

Step-by-step explanation:

Let x be the number of people initially. We can find the amount each of them has to pay at first

2 / x

But when 10 people walk away, the remaining (x - 10) has to pay 10 cents more to get the same total of $2. This would means

$(\frac{2}{x} + 0.1)(x-10) = 2$

From here we can perform cross multiplication

$2 - 20/x + 0.1x - 1 = 2$

$0.1x - 20/x - 1 = 0$

Multiply both sides by 10x:

$x^2 -10x - 200 = 0$

$x= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

$x= \frac{10\pm \sqrt{(-10)^2 - 4*(1)*(-200)}}{2*(1)}$

$x= \frac{10\pm30}{2}$

x = 20 or x = -10

Since x can only be positive we will pick x = 20