Example Card: Application with Averages
Apply application with averages in Grade 9 math — How can we use inequalities to find a missing data point for a desired average? Part of Quadratic Functions and Equations for Grade 9.
Key Concepts
How can we use inequalities to find a missing data point for a desired average?
Example Problem For a student to earn a B, their average on 4 tests must be between 80 and 89, inclusive. Their first three test scores are 78, 85, and 81. What score is needed on the fourth test?
Step by Step 1. First, set up a compound inequality to represent the situation. Let $x$ be the score on the fourth test. $$ 80 \le \frac{78 + 85 + 81 + x}{4} \le 89 $$ 2. Simplify the sum of the known scores in the numerator. $$ 80 \le \frac{244 + x}{4} \le 89 $$ 3. To clear the fraction, multiply all three parts of the inequality by $4$. $$ 4 \cdot 80 \le 4 \cdot \frac{244 + x}{4} \le 4 \cdot 89 $$ 4. Simplify the multiplication in each part. $$ 320 \le 244 + x \le 356 $$ 5. To isolate $x$, subtract $244$ from all three parts of the inequality. $$ 320 244 \le 244 + x 244 \le 356 244 $$ 6. Perform the subtraction to find the range of possible scores for the fourth test. $$ 76 \le x \le 112 $$ The student must score between a 76 and a 112 on the fourth test.
Common Questions
What is 'Application with Averages' in Grade 9 math?
How can we use inequalities to find a missing data point for a desired average? Their first three test scores are 78, 85, and 81.
How do you solve problems involving 'Application with Averages'?
Their first three test scores are 78, 85, and 81. First, set up a compound inequality to represent the situation.
Why is 'Application with Averages' an important Grade 9 math skill?
Common mistake tip: A very common mistake is to only apply the operations (like multiplying by 4 or subtracting 265) to the two outer parts of the inequality and forget the middle.. Whatever you do to one part, you must do it to all three parts to keep the inequality true!.