Xavier could buy 65 identical basketballs with all his money. When the price of each ball was increased by $5, he could buy 20 fewer balls. How much money did Xavier have?
Let's start by using algebra to solve the problem.
Let x be the original price of one basketball.
Then we know that Xavier's money can buy 65 basketballs at the original price, which means:
65x = Xavier's total amount of money
When the price of each ball goes up by $5, the new price becomes x + 5.
Now Xavier can only buy 20 fewer balls, which means:
(65-20)(x+5) = Xavier's total amount of money
45(x+5) = 65x
45x + 225 = 65x
20x = 225
x = 11.25
So the original price of one basketball was $11.25.
Now we can use this to find out how much money Xavier had:
65x = 65(11.25) = $731.25
Therefore, Xavier had $731.25.
Let's assume the initial price of each basketball was $x.
According to the given information, Xavier could buy 65 identical basketballs with all his money, so we can write the equation:
65x = Xavier's money
After the price increased by $5, the new price of each basketball became $(x + 5).
With this new price, Xavier could buy 20 fewer balls, so we can write the equation:
(x + 5)(65 - 20) = Xavier's money
Now, let's solve the equations simultaneously to find the value of x:
65x = (x + 5)(45)
Expanding the right side of the equation:
65x = 45x + 225
Subtracting 45x from both sides:
20x = 225
Dividing both sides by 20:
x = 225/20
Therefore, the initial price of each basketball (x) is $11.25.
Substituting this value back into the first equation to find Xavier's money:
65 * 11.25 = $731.25
Therefore, Xavier had $731.25.