Finding the Average: Calculating a Biology Class's Weighted Grade

A biology class receives the following grades:



What is the class average?

To solve this problem, we will calculate the weighted average based on the following given data and constraints:

• Grade 75 with a weight of 30%.

• Grade 68 with a weight of 20%.

• Grade 94 with a weight of $X\%$.

• Grade 53 making up the remaining percentage, which equals $100\% - (30\% + 20\% + X\%) = (50 - X)\%$.

Now, we perform the calculations step by step:

1. Convert percentages to decimals:

• 30% becomes 0.30, 20% becomes 0.20, $X\%$ becomes $\frac{X}{100}$, and $(50 - X)\%$ becomes $\frac{50-X}{100}$.

2. Calculate the weighted value of each grade:

• Grade 75: $75 \times 0.30 = 22.5$.

• Grade 68: $68 \times 0.20 = 13.6$.

• Grade 94: $94 \times \frac{X}{100} = 0.94X$.

• Grade 53: $53 \times \frac{50-X}{100} = 0.53(50 - X) = 26.5 - 0.53X$.

3. Sum these weighted values to get the overall weighted average:

$\text{Weighted Average} = 22.5 + 13.6 + 0.94X + 26.5 - 0.53X$

This simplifies to:

$62.6 + 0.41X$

Thus, the class average can be expressed as $62.6 + 0.41X$.