Question 322012: Angie bought some golf balls for $24. If each ball had cost $0.50 less, she could have purchased one more ball for the same amount of money. How many golf balls did Angie buy?
Answer by nyc_function(2741)   (Show Source):
You can put this solution on YOUR website!
Here is another method:
Let n = number of balls purchased
Let p = price per ball
Therefore:
n * p = 24
(n + 1)(p - 0.5) = 24
Therefore:
p = 24/n
(n + 1)((24/n) - 0.5) = 24
24 - 0.5n + (24/n) - 0.5 = 24
-0.5n + (24/n) - 0.5 = 0
Multiply through by -2n:
n^2 + n - 48 = 0
n = (-1 +/- sqrt(1^2 - 4(1)(-48))) / (2*1)
n = (-1 +/- sqrt(1 + 192)) / 2
n = (-1 +/- sqrt(193)) / 2
n = -0.5 +/- sqrt(48.25)
n =~ 6.47 or -7.47
Suppose she bought 6 balls, so they each cost $4. If they had cost $3.50, then $24 would still not be enough to buy 7 balls. So that doesn't work.
Suppose she bought 7 balls, so they each cost about $3.43. If they had cost $2.93, she could have bought 8 balls for $24 (and received $0.56 in change).
Suppose she bought 8 balls, so they each cost $3. If they had cost $2.50, she could have bought 9 balls for $24 (and received $1.50 in change).
Suppose she bought 9 balls, so they each cost about $2.67. If they had cost $2.17, she could have bought at least 11 balls for $24. So that doesn't work.
So the answer must be 7 (or 8).
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