Let's break down the problem and work through the calculations:

Weight distribution:

• Coursework (5 tests): 70%
• CPT (Culminating Performance Task): 10%
• Exam: 20%

You have already taken 3 of the 5 coursework tests. You need to figure out the grades required for the last two coursework tests to achieve an overall average of 95%.

Step 1: Current information

• Test 1: 83
• Test 2: 87
• Test 3: 86
• Tests' weight: 70%

The average of the 5 tests will contribute to 70% of the final grade.

Let the grades of the remaining two tests be $x_4$ and $x_5$.

Step 2: Desired overall average

You want a final overall average of 95.

The formula for the overall final grade is:

$\text{Final Grade} = \left(\frac{\text{Average of 5 tests}}{100} \times 70\right) + \left(\frac{\text{CPT}}{100} \times 10\right) + \left(\frac{\text{Exam}}{100} \times 20\right)$

This final grade must equal 95.

Step 3: Average of the 5 tests

The average of the 5 tests is:

$\text{Average of 5 tests} = \frac{83 + 87 + 86 + x_4 + x_5}{5}$

Step 4: Plugging it all together

For simplicity, let's assume you get 95 on both the CPT and the Exam, as you haven't provided these scores but need to maintain a 95% overall average.

So, the equation becomes:

$95 = \left(\frac{83 + 87 + 86 + x_4 + x_5}{5} \times \frac{70}{100}\right) + \left(\frac{95}{100} \times 10\right) + \left(\frac{95}{100} \times 20\right)$

Let's solve this equation to find out what grades you need on the remaining two tests. I'll calculate it now.It appears there was an issue with solving for the exact grades in the symbolic approach. Let me adjust and recalculate manually for the grades required on the last two tests to achieve the desired 95 average, assuming a 95% in both the CPT and the exam.

I'll simplify the equation step by step.To achieve a 95% overall average, the sum of the grades for your last two tests must total 219. This means the combined grades of the last two tests should be 219, so you could aim for two grades that add up to this, like 109.5 each, or some combination (e.g., 110 and 109).

Let me know if you need further clarification or more details!

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Here are 5 related questions that expand on this:

1. What happens if I score less than 95 on the CPT or exam?
2. Can you explain how weighting affects the final average in more detail?
3. How would changing the weight of coursework alter the required test grades?
4. What strategies can help improve performance on upcoming tests?
5. What would my average be if I scored 90 on the last two tests instead?

Tip: Focus on improving study techniques for the last two tests, as high performance there will be crucial to reaching your goal.