1.Based on the given information, the original group of tourists consisted of 7 people.
2. Esirkep expected the job to take 6 hours.
How to find the number of tourists
1.Assume that there were initially "x" tourists in the original group.
If each tourist shared equally in the $14,000 cost of the boat, the cost per tourist would be $14,000 / x.
When three tourists decide not to pay, the remaining tourists have to cover their share, which increases the cost per tourist by $1500.
So, after three tourists drop out, the new cost per tourist is $14,000 / (x - 3).
According to the given information, the new cost per tourist is $1500 more than the initial cost per tourist:
$14,000 / (x - 3) = $14,000 / x + $1500
To solve this equation, multiply both sides by x(x - 3) to eliminate the denominators:
$14,000 * x = $14,000 * (x - 3) + $1500 * x(x - 3)
Simplifying the equation:
14,000x = 14,000x - 42,000 + 1500x² - 4500x
Rearrange the terms and equate it to 0
0 = 1500x² - 4500x - 42,000
Divide the equation by 1500 to simplify:
0 = x² - 3x - 28
Now, solve this quadratic equation by factoring or using the quadratic formula.
Factoring the equation, we have:
0 = (x - 7)(x + 4)
Setting each factor equal to zero:
x - 7 = 0 or x + 4 = 0
x = 7 or x = -4
Since the number of tourists cannot be negative, we discard x = -4 as an extraneous solution.
Therefore, the original group of tourists consisted of 7 people.
2.
Let's assume that Esirkep expected the job to take "x" hours.
According to the given information, he ended up taking seven hours longer than expected, so the actual time it took to complete the job is x + 7 hours.
Additionally, Esirkep earned $14 per hour less than he anticipated, so his actual hourly rate is $14 less than his expected rate.
Now, calculate the total earnings in two different ways:
Expected earnings: x hours * expected hourly rate = x * (expected rate)
Actual earnings: (x + 7) hours * actual hourly rate = (x + 7) * (expected rate - $14)
Since Esirkep earned $156, set up the equation:
x * (expected rate) = (x + 7) * (expected rate - $14) = $156
x * (expected rate) = x * (expected rate - $14) + 7 * (expected rate - $14) = $156
expected rate = expected rate - $14 + 7 * (expected rate - $14) / x = $156 / x
Simplifying the equation:
$14 = 7 * (expected rate - $14) / x
$14x = 7 * (expected rate - $14)
Divide both sides by 7:
2x = expected rate - $14
Substitute the value of the expected rate in terms of x:
2x = $156 / x - $14
Multiplying through by x:
2x² = $156 - $14x
Rearrange the equation:
2x² + $14x - $156 = 0
Divide the equation by 2 to simplify:
x² + 7x - $78 = 0
Now, solve this quadratic equation by factoring or using the quadratic formula.
Factoring the equation, we have:
(x - 6)(x + 13) = 0
Set each factor equal to zero:
x - 6 = 0 or x + 13 = 0
Solving for x in each case:
x = 6 or x = -13
Since the expected time cannot be negative, we discard x = -13 as an extraneous solution.
Therefore, Esirkep expected the job to take 6 hours.