write an equation to represent the situation: if a player made 12 out of 15 free throws, how many consecutive free throws would she have to make to raise the percent to 85%.
12+x = .85(15+x)
Let's first define the variables in the equation:
x = number of consecutive free throws the player needs to make
n = total number of free throws attempted (in this case, n = 15)
To find the equation, we need to consider the percentage of successful free throws that the player needs to reach. In this case, the player wants to raise the percentage to 85%.
The equation can be derived as follows:
(12 + x) / (15 + x) = 85 / 100
Explanation: The numerator represents the total successful free throws, which is the sum of the current successful free throws (12) and the additional consecutive successful free throws (x). The denominator represents the total number of attempts, which is the sum of the current attempts (15) and the additional attempts (x). The right side of the equation represents the desired percentage of successful free throws (85%).
Simplifying the equation, we can cross multiply:
(12 + x) * 100 = (15 + x) * 85
Expanding both sides:
1200 + 100x = 1275 + 85x
Now, solve for x:
100x - 85x = 1275 - 1200
15x = 75
Divide both sides by 15:
x = 5
Therefore, the player would need to make 5 consecutive free throws to raise the percentage to 85%.
To represent this situation with an equation, we can use the following steps:
Step 1: Let's assume the number of consecutive free throws the player must make to raise the percent to 85% is represented by the variable "x".
Step 2: The player made 12 out of 15 free throws, so the total number of successful free throws is 12 + x (the additional consecutive free throws).
Step 3: The total number of attempts, considering the consecutive free throws, would be 15 + x (the initial 15 attempts plus the additional consecutive attempts).
Step 4: We can now construct the equation based on the percentage formula:
(12 + x) / (15 + x) = 85 / 100
Here, (12 + x) represents the successful free throws and (15 + x) represents the total attempts. 85/100 is used to represent 85% as a decimal.
This equation can be used to solve for the value of "x," which will determine the number of consecutive free throws the player needs to make to raise their free throw percentage to 85%.