A group of tourists agree to share the cost of chartering a boat to an island. At the last moment, one of them gets out, resulting in each of the remaining tourists having to pay RM10 more. If the cost of chartering the boat is RM120, Hoe many tourists are there at the beginning.
This question is extracted from Quadratic Equation. I seriously don't know how to form the equation out. Hope that someone will explain it. Thanks in advance.
There are $x $ guests at the beginning so the share at the beginning is $$S_1 =120/x $$ Now after one gets out there are $x-1$ remaining. Then the share $$S_2=\frac {120 }{x-1} $$ It is now given that $$S_2-S_1=10$$ $$\Rightarrow \frac{120}{x-1}-\frac {120 }{x}=10$$ Can you take it from here? The answer is $\boxed {x=4} $. Hope it helps.
Let initially x tourists.
Then each contribute $\frac{120}{x}$
Now 1 tourist left. So remaining (x - 1) tourists.
Now each contribute $\frac{120}{x - 1}$
According to question
New contribution - Old contribution = 10
$\frac{120}{x - 1} - \frac{120}{x} = 10$
$120\left(\frac{1}{x - 1} - \frac1{x}\right) = 10$
$120\left(\frac{x - x + 1}{x(x - 1)}\right) = 10$
$12\left(\frac{1}{x(x - 1)}\right) = 1$
$12 = x(x - 1)$
$x^2 - x - 12 = 0$
$x^2 - 4x + 3x - 12 = 0$
$(x - 4)(x + 3) = 0$
x = 4