SOLUTION: Can someone help me solve this problem? A museum curator can use the equation C = 3x + square root of (50x + 9000) to find the cost C (in dollars) for taking x people on a tour

Question 1111721: Can someone help me solve this problem?
A museum curator can use the equation C = 3x + square root of (50x + 9000) to find the
cost C (in dollars) for taking x people on a tour of the museum.
16. If the cost is $160, how many people went on a tour?
17. If the curator charges each person $10 to go on the tour, write an
expression for the revenue generated.
18. How many people must go on the tour for the curator to break even?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
16) 160 = 3x + square root of (50x + 9000)
:
3x + square root of (50x + 9000) = 160
:
square root of (50x + 9000) = 160 -3x
:
square both sides of the =
:
50x + 9000 = 25600 -960x +9x^2
:
9x^2 -1010x +16600 = 0
:
factor the equation
:
(x-20) * (9x-830) = 0
:
x -20 = 0
:
x = 20
:
9x-830 = 0
:
x = 830/9
:
*****************************************************************************
reject the fraction answer(it does not solve equation), 20 people went on tour
*****************************************************************************
:
17) Revenue = 10x
:
18) 10x = (3x + square root of (50x + 9000))
:
square root of (50x + 9000) = 7x
:
x = 14
:
14 people is the break even point
:

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