Question 1173213: The event manager collected a total amount of not more than $40,000 from more than 200 adults and children who watched a basketball game. Tickets for that game cost
$150 for adults and $100 for children. Around how many adults and children watched the game?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your constaints are:
x + y > 200
150x + 100y <= 40000
x >= 0
y >= 0
using the desmos.com calculator, you would graph the opposite of these inequalities.
any point in the unshaded area of the graph and on the line line of 150x + 100y = 40000 that borders the unshaded area of the graph is valid.
3 valid points are:
3 points that are valid are (0,400), (266.667,0) and (60,260).
these points have to meet the requirements of the constraint inequalities.
they're all greater than or equal to 0, so those requirements are met.
x + y must be > 200.
that requirement is met at all of the points mentioned since x + y is greater than 200 at all of those points.
150x + 100y <= 40,000 has to be met at all of the points mentioned.
150x + 100y <= 40,000 is evaluated at each of those points.
(0,400) = 100 * 400 = 40,000 which meets the requirements.
266.667 * 150 = (266 + 2/3) * 150 = 800/3 * 150 <= 40,000 becomes 40,000 <= 40,000 which meets the requirements.
(60,260) = 150 * 60 + 150 * 260 = 35,000 <= 40,000, so that meets the requirements.
all the points meet the requirement, so all of the points are valid.
the point (266.667,0), however does not lead to a whole number.
that number should be rounded down or up to make it a whole number.
(266,0) = 266 * 150 = 39900 <= 40,000, so rounding down is good.
(267,0) = 267 * 150 = 40,050 which is not <= 40,0009, so rounding up is not good.
the 3 valid points that are whole numbers that meet the requirements are (0,400), (266,0), (60,260).
around how many adults and children watched the game?
that number should be a minimum of 201 to a maximum of 400.
both numbers will get you x + y > 200
both numbers will get you 150x + 100y <= 40,000
maximum revenue with 0 adults and 400 children attending is 400 * 100 = 40,000.
this meets the requirements.
maximum revenue with 266 adults and 0 children attending is 266 * 150 = 39,900.
this meets the requirements.
unless i'm missing something, i don't think you can answer this equation with one number.
there is a range of numbers.
those numbers have to be in the unshaded portion of the graph as described above and shown below.
that's my opinion.
here's the graph.
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