Final answer:
A man bought 2 golf balls.
To determine the initial quantity of golf balls bought for $20, we set up a system of equations based on the given conditions and solve for the variables representing the number of balls and cost per ball.
Step-by-step explanation:
Let's assume the number of golf balls he bought is x.
According to the given information, the total cost of x number of golf balls is $20.
If each ball had cost 20 cents less, he could have bought five more for the same money.
So, the new price of each ball would be 20 cents less than the original price.
Therefore, the cost of 5 extra golf balls would be $20.
We can set up the equation: (x + 5)(original price - $0.20) = $20.
Simplifying this equation, we get x(original price) - $0.20x + 5(original price) - $1 = $20.
Combining like terms, we have x(original price) + 5(original price) - $0.20x - $1 = $20.
x(original price) - $0.20x + 5(original price) - $1 = $20.
x(original price) + 5(original price) - $0.20x - $1 = $20.
Combining like terms, we have 6(original price) - $0.20x - $1 = $20.
Adding $1 to both sides of the equation, we get 6(original price) - $0.20x = $21.
Subtracting $21 from both sides of the equation, we get 6(original price) - $0.20x - $21 = 0.
Now, we can solve this quadratic equation to find the value of x.
Using the quadratic formula, x = (-(-$0.20) + sqrt((-0.20)^2 - 4(6)(-$21)) / (2(6)).
Simplifying further, x = ($0.20 + sqrt(0.04 + 504)) / 12.
x = ($0.20 + sqrt(504.04)) / 12.
x = ($0.20 + 22.44) / 12.
x = $22.64 / 12.
x = 1.8867.
Since the number of golf balls cannot be a decimal, we can conclude that he bought 2 golf balls.