Chelsea had made six of seventeen free-throw attempts. How many consecutive free throws must she make to raise her percentage of free throws made to exactly 50 percent?
(6+x)/(17+x) = 1/2
12 + 2x = 17+x
x = 5
check:
with 5 more successful throws she made 11 good ones
out of a total of 17+5 or 22
11/22 is 50%
To solve this problem, follow these steps:
Step 1: Find the current percentage of free throws made. Divide the number of successful attempts (6) by the total number of attempts (17) and multiply by 100:
Current percentage = (6/17) * 100 = 35.29%
Step 2: Calculate the number of consecutive successful attempts needed to reach a 50% success rate. Let's call this value 'x':
(6+x)/(17+x) = 0.50
Step 3: Solve the equation for 'x' using algebra:
6 + x = 0.50 * (17 + x)
6 + x = 8.5 + 0.50x
0.50x - x = 8.5 - 6
-0.50x = 2.5
x = 2.5 / (-0.50)
x = -5
Step 4: Interpret the result. Since we can't have a negative number of consecutive successful attempts, we conclude that Chelsea would need to make zero consecutive free throws to raise her percentage of free throws made to exactly 50 percent.
To determine how many consecutive free throws Chelsea must make to raise her percentage of free throws made to exactly 50 percent, we need to find the number of successful free throws out of the total attempts that will result in a 50 percent success rate.
First, we must calculate Chelsea's current free throw percentage. We can do this by dividing the number of successful free throws by the total attempts and multiplying by 100:
Free throw percentage = (successful free throws / total attempts) * 100
In this case, Chelsea made 6 out of 17 free throw attempts, so her current free throw percentage is:
(6 / 17) * 100 = 35.29%
To raise her percentage to exactly 50%, we need to find the number of consecutive successful free throws that will result in this new percentage.
Let's represent the number of consecutive successful free throws as 'x'. This means Chelsea will have made 6 + x successful free throws. The total number of attempts will be 17 + x.
To calculate the new free throw percentage, we'll use the following equation:
new free throw percentage = (successful free throws / total attempts) * 100
Substituting the values, we get:
50 = (6 + x) / (17 + x) * 100
To solve for 'x', we need to isolate it on one side of the equation:
50(17 + x) = (6 + x) * 100
850 + 50x = 600 + 100x
50x - 100x = 600 - 850
-50x = -250
x = -250 / -50
x = 5
Therefore, Chelsea needs to make 5 consecutive free throws to raise her free throw percentage to exactly 50 percent.