Calculate Javier's Weighted Exam Score: Solve for x when 0.55x + 0.45(76) = 84

How much does Javier score on the first exam that has a weight of 55%, given that he scores 76 on the second exam and his final average is 84?

To solve this problem, we'll proceed with the following steps:

• Step 1: Define the weights and scores for each exam.
• Step 2: Formulate the equation for the weighted average.
• Step 3: Solve the equation for $x$, the unknown score on the first exam.

Now, let's work through each step:

Step 1: We know:

• Weight of the first exam: $0.55$
• Weight of the second exam: $0.45$
• Score on the second exam: $76$
• Final average score: $84$
• Unknown score (first exam): Let it be $x$

Step 2: We use the weighted average formula:

Step 3: Now solve for $x$.

First, calculate the contribution of the second exam:

Substitute this back into the equation:

Subtract 34.2 from both sides to solve for $0.55 \times x$:

Finally, divide both sides by 0.55 to isolate $x$:

Calculate the result:

Therefore, the solution to the problem is $\mathbf{90.55}$.