SOLUTION: 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?

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).

RELATED QUESTIONS
Angie bought some golf balls for $3. If each ball had cost $0.25 less, she could have... (answered by richwmiller)

1. George has $700 to invest. Suppose he invests $300 at 6% interest. At what rate must... (answered by VFBundy,MathTherapy)

Angie bought some candy bars for $14. If each candy bar had cost $0.25 less, she could... (answered by lwsshak3)

The coach purchased b balls for d dollars. If each ball had cost $2 more, how many balls (answered by stanbon)

Last week Al bought some golf balls for $20. The next day they were on sale for $0.50 per (answered by stanbon)

A storeowner buys a quality of balls for $600. If they had each cost $0.25 less, shewould (answered by sujatha.krishna)

If Sarah paid $36 for a dozen golf balls, what is the cost for one... (answered by rfer)

A storeowner buys a quantity of tennis ball for $600. If they had each cost $0.25 less,... (answered by josmiceli)

a student bought some packets of pen for 2000 dollar. if she had paid 24 dollar less for... (answered by ankor@dixie-net.com)