Question

A certain travel agency offered a tourthat will cost each person P 1500.00 if not more than 150 persons will join,however the cost per person will be reduced by P 5.00 per person in excessof 150. what will be the maximum profit?

Answer 1

Number of people in excess of 150 ---- x
number of people on tour = x + 150
total cost = 150(1500) + x(1500-5x)
= 225000 + 1500x - 5x^2

find the vertex of this downwards opening parabola using the method you learned. The y-coordinate will be you maximum cost, (not profit as you stated)

This question makes little sense to me. If the current cost per person is 1500 each for the first 150 people, and it reduces by 5 per person for over the 150 mark, wouldn't the cost per person go down to zero if 450 people joined the tour??
that is, number of people over 150 = 300
reduction in cost per person = 300(5) = 1500
so cost = 1500-1500 = 0

check the wording of the question.

Answer 2

I also find it strange that this same question appeared in that identical form back in 2016 including the same spelling and punctuation error.

https://www.jiskha.com/questions/1412396/A-certain-travel-agency-offered-a-tourthat-will-cost-each-person-P-1500-00-if-not