Problem Analysis:
The problem involves determining whether a basketball player can achieve a free throw shooting percentage greater than 75% after making their first 5 free throws and missing the rest. The player shot a total of 8 free throws in the game. We are tasked with solving this using an inequality.
Known Information:
1. The player made
5 free throws out of a total of
8 free throws.
2. The player missed the remaining free throws, which is \( 8 - 5 = 3 \).
3. The goal is to have a free throw shooting percentage
greater than 75%.
4. The formula for the shooting percentage is:
\[
\text{Shooting Percentage} = \frac{\text{Number of Free Throws Made}}{\text{Total Number of Free Throws Attempted}}
\]
5. We need to check if the shooting percentage exceeds 75%, i.e.,:
\[
\frac{\text{Number of Free Throws Made}}{\text{Total Number of Free Throws Attempted}} > 0.75
\]
Step-by-Step Solution:
#### Step 1: Define Variables
Let:
- \( x \) represent the number of free throws missed.
- The total number of free throws attempted is 8.
- The number of free throws made is \( 8 - x \).
From the problem, we know:
- The player made 5 free throws.
- The player missed \( x = 3 \) free throws.
#### Step 2: Set Up the Inequality
The shooting percentage must be greater than 75%. This can be expressed as:
\[
\frac{\text{Number of Free Throws Made}}{\text{Total Number of Free Throws Attempted}} > 0.75
\]
Substitute the known values:
\[
\frac{5}{8} > 0.75
\]
#### Step 3: Convert 0.75 to a Fraction
To compare fractions easily, convert 0.75 to a fraction:
\[
0.75 = \frac{75}{100} = \frac{3}{4}
\]
#### Step 4: Compare Fractions
Now, compare \( \frac{5}{8} \) and \( \frac{3}{4} \):
- Convert \( \frac{3}{4} \) to a fraction with a denominator of 8:
\[
\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}
\]
- Compare \( \frac{5}{8} \) and \( \frac{6}{8} \):
\[
\frac{5}{8} < \frac{6}{8}
\]
#### Step 5: Conclusion
Since \( \frac{5}{8} < \frac{6}{8} \), the shooting percentage is less than 75%. Therefore, the player did not meet the goal of having a shooting percentage greater than 75%.
Final Answer:
\[
\boxed{\text{No}}
\]
Parent Tip: Review the logic above to help your child master the concept of rational equation word problems worksheet.
