Final answer:
To solve the problem, we set up an equation based on the given information, then solved the quadratic equation to find the number of people who went on the expedition.
Step-by-step explanation:
The question requires solving an algebraic problem to determine the number of people who went on the climbing expedition. We start with setting up an equation. Let the original number of people scheduled to go be x. Therefore, the cost per person before the 2 people dropped would be $2800 divided by x. After the two people dropped out, the number of people going became x-2, and the cost per person increased by $70, making the new cost per person $2800 divided by x-2.
The new cost per person is the old cost per person plus $70. So we have:
$2800/x + $70 = $2800/(x-2)
Then we multiply all terms by x(x-2) to clear the denominators:
$2800(x-2) + $70x(x-2) = $2800x
$2800x - $5600 + $70x^2 - $140x = $2800x
Now we move all terms to one side to set the equation to zero and combine like terms:
$70x^2 - $140x - $5600 = 0
To make it easier to solve, we divide all terms by $70 to simplify the equation:
x^2 - 2x - 80 = 0
This is a quadratic equation, and we can factor it as:
(x-10)(x+8) = 0
Since we cannot have a negative number of people, we ignore the solution x+8=0 and take the positive solution x-10=0, thus x = 10. Therefore, 10 people went on the climbing expedition after the two members dropped out.