can you please help me solve this 😭😭

Question

a group of youth intends to fish in the lake near the island of Tioman. The total cost for boat hire and preparation is RM 2520 and they share pay equally. At the last minute, 4 of them canceled the trip, the remaining youngsters had to pay a fee of RM224 each. State the number of youth who are still following the journey. Describe the methods used and show the calculations.

Answer 1

Let p = number persons originally attending

Let c = original cost per person

 

Number of persons will be the total cost of 2520 divided by the original cost per person, c:

 

p = total/(cost per person)

p = 2520/c    {equation 1}

 

When the number of persons decreased by 4, the cost per person increased by 224:

 

p-4 = 2520/(c+224)   {equation 2}

 

Replace p with 2520/c in equation 2 and solve for c:

 

2520/c - 4 = 2520/(c+224)

Get common denominator on left side

(2520 - 4c)/c = 2520/(c + 224)

Cross multiply

2520c = (2520-4c)(c + 224)

Distribute the parenthesis on the right side with FOIL

2520c = 2520c + 2520(224) - 4c² - 896c

Subtract 2520c from both sides

0 = -4c² - 896c + 564480

For ease of working I multiplied both sides by -1

4c² + 896c - 564480 = 0

All numbers are factorable by 4 so divide both sides by 4

c² + 224c - 141120 = 0  

 

Using quadratic equation:  Given ax² + bx + c = 0

                                       x = [-b ±√(b²-4ac)]/2a

 

c = [-224 ±√(224²-4(-141120))]/2

 

c = (-224 ±√614656)/2

 

c = (-224 ± 784)/2

 

Disregarding the negative since the cost will be a positive quantity:

 

c = (784-224)/2

 

c = 560/2

 

c = 280    The original cost per person was RM 280

 

p = 2520/c = 2520/280 = 9   Originally 9 persons were supposed to go

 

4 cancelled meaning 5 persons actually went