SOLUTION: a man purchased a number of balloons, each of the same price, for a total of $720. he sold them all at $40 each, thus realizing a profit equal to his 8 balloons. how many did he bu

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Question 126925: a man purchased a number of balloons, each of the same price, for a total of $720. he sold them all at $40 each, thus realizing a profit equal to his 8 balloons. how many did he buy?
can you solve this using the quadratic equation??? thanks!!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
a man purchased a number of balloons, each of the same price, for a total of $720. he sold them all at $40 each, thus realizing a profit equal to his 8 balloons. how many did he buy?
can you solve this using the quadratic equation??? thanks!!
:
Let's write down what we know here:
:
Let x = no. of balloons purchased
:
Price he paid for each = 720%2Fx
:
Profit given as: 8(720%2Fx)
:
Revenue from the sale of all the balloons = 40x
:
Revenue - cost = profit
40x - 720 = 8(720/x)
:
40x - 720 = 5760/x
:
40x^2 - 720x = 5760; multiplied equation by x to get rid of the denominator
:
40x^2 - 720x - 5760 = 0 the quadratic equation you so earnestly desired.
:
x^2 - 18x - 144 = 0 simplified, divided equation by 40
Factor to:
(x - 24)(x + 6) = 0
The positive solution is what we want:
x = 24 balloons
:
:
His cost for each balloon: 720%2F24 = $30
Check solution in the profit equation
40(24) - 720 = 8(30)
960 - 720 = 240; confirms our solution
:
How about this? Did it make sense to you? Any questions?