Katie makes 65% of her shots from the free throw line. Can you determine how many consecutive free throws she must make in order to increase her percentage to 68%? Explain.
no
if she made 65 out of 100 that will take less than if she made 650 out of 1000
Hard to say. If she has made 65% of n throws so far, then she needs to throw x more in a row to get to 68%.
.65n + x = .68(n+x)
.03n = .32x
x = 3/32 n
To determine the number of consecutive free throws Katie must make in order to increase her shooting percentage, we can set up an equation.
Let's assume Katie has attempted a total of x free throws so far. From the given information, we know that she makes 65% of her shots, which means she makes 0.65x free throws.
Now, let's consider the scenario where Katie makes y consecutive free throws without missing. Her total successful free throws would then increase to 0.65x + y.
To calculate Katie's new shooting percentage, we divide the total successful free throws (0.65x + y) by the new total attempts (x + y):
New shooting percentage = (0.65x + y) / (x + y)
According to the problem, we want this new shooting percentage to be 68%. So we can set up the equation:
0.68 = (0.65x + y) / (x + y)
Now let's solve for y, the number of consecutive free throws she must make:
0.68(x + y) = 0.65x + y (multiplying both sides by x + y to eliminate the denominator)
0.68x + 0.68y = 0.65x + y (distributing on the left side)
0.68y - y = 0.65x - 0.68x (grouping the variables together)
0.68y - y = (0.65 - 0.68)x (combining like terms)
0.68y - y = -0.03x (simplifying the right side)
Now, we can isolate y by moving -0.03x to the left side:
0.68y - y + 0.03x = 0
0.68y - y = -0.03x
0.68y = y - 0.03x
0.68y - y = -0.03x
(0.68 - 1)y = -0.03x
-0.32y = -0.03x
Dividing both sides by -0.32:
y = (-0.03x) / (-0.32)
y = (0.03x) / (0.32)
y = 0.09375x
Therefore, Katie must make approximately 0.09375 (which is close to 1/11) times the number of total free throws she has attempted to increase her shooting percentage to 68%.
Sure! To determine how many consecutive free throws Katie must make in order to increase her shooting percentage, we can use the following steps:
Step 1: Determine the current shooting percentage:
Katie currently makes 65% of her shots from the free throw line. This means she makes 65 out of every 100 shots.
Step 2: Determine the number of successful shots:
To find out the number of successful shots Katie has made so far, we multiply her shooting percentage by the total number of shots attempted. Let's assume she has attempted "x" shots.
Successful shots = (65/100) * x
Step 3: Determine the number of unsuccessful shots:
The number of unsuccessful shots can be obtained by subtracting the successful shots from the total number of shots attempted.
Unsuccessful shots = x - (65/100) * x = (35/100) * x
Step 4: Set up the equation:
Now we need to set up an equation to find how many consecutive free throws Katie must make to increase her shooting percentage to 68%. The equation can be formed as:
[(successful shots + consecutive successful shots) / (total shots + consecutive successful shots)] * 100 = 68
Step 5: Solve the equation:
Substituting the values we have, the equation becomes:
[(successful shots + consecutive successful shots) / (x + consecutive successful shots)] * 100 = 68
Now we can solve this equation to determine the number of consecutive successful shots Katie must make.
I hope these steps explain how to determine the number of consecutive free throws Katie must make in order to increase her shooting percentage to 68%!