The student got 24 out of 50 on test 1 and 19 out 20 on quiz one, how much should she get on the 2 remaining tests out of 50 and one quiz out of 20 to get 70% year mark according to the rule below

Question

Each semester test is out of 50. You need to work each out to be a percentage. Then multiply each test's percentage with 0.3 (30%) as each test contributes 30% towards your final mark. Then you have to take your best 2 quiz marks, and work them each out to a percentage. Then either multiply each of the two quizzes percentages by 0.05 (5%) weight or get the average of the two and multiply that percentage by 0.1 (10%) as the quizzes contribute 10% to the final mark. You then add all these marks together.

Answer 1

To determine how much the student needs to score on the remaining tests and quiz to achieve a final mark of 70%, we will follow the grading structure provided.

Step 1: Calculate Current Scores

The student has completed one test and one quiz:

• Test 1: \[ \text{Percentage for Test 1} = \left( \frac{24}{50} \right) \times 100 = 48% \]
• Quiz 1: \[ \text{Percentage for Quiz 1} = \left( \frac{19}{20} \right) \times 100 = 95% \]

Step 2: Current Contributions to Final Mark

Let's establish how much the current scores contribute to the final mark calculation.

Contribution from Test 1: \[ \text{Contribution from Test 1} = 48% \times 0.3 = 14.4 \]

Quiz Contribution (assuming this is the only quiz so far): \[ \text{Contribution from Quiz 1} = 95% \times 0.05 = 4.75 \]

So far, the total contribution to the final mark is: \[ \text{Total Contribution} = 14.4 + 4.75 = 19.15 \]

Step 3: Contribution Required for Final Mark of 70%

The required final mark is 70%. The contributions to the final mark come from two tests and two quizzes, meaning 30% for three tests and 10% for two quizzes. The remaining contributions must equal \(70 - 19.15\).

Let \(T_2\) be the percentage of Test 2, \(T_3\) be the percentage of Test 3, and \(Q_1\) be the percentage of the next quiz.

We want: \[ T_2 \times 0.3 + T_3 \times 0.3 + Q_1 \times 0.05 \geq 70 - 19.15 \] This simplifies to: \[ T_2 \times 0.3 + T_3 \times 0.3 + Q_1 \times 0.05 \geq 50.85 \]

Step 4: Solve for Remaining Tests and Quiz

Assume the student scores \(x\) on both remaining tests and \(y\) on the quiz.

Then the inequality becomes: \[ x \times 0.3 + x \times 0.3 + y \times 0.05 \geq 50.85 \] or simplified: \[ 0.6x + 0.05y \geq 50.85 \] Now, let’s isolate \(y\): \[ 0.05y \geq 50.85 - 0.6x \] \[ y \geq \frac{50.85 - 0.6x}{0.05} \] \[ y \geq 1017 - 12x \]

Step 5: Example Calculations

1. If \(x = 50\) (highest score possible): \[ y \geq 1017 - 12 \times 50 = 1017 - 600 = 417 \quad (\text{not possible, max is 100%}) \]

2. If \(x = 40\): \[ y \geq 1017 - 12 \times 40 = 1017 - 480 = 537 \quad \text{(not possible)} \]

3. If \(x = 35\): \[ y \geq 1017 - 12 \times 35 = 1017 - 420 = 597 \quad \text{(not possible)} \]

Continue checking values down to reasonable scores until \(x < 25\).

4. If \(x = 25\): \[ y \geq 1017 - 12 \times 25 = 1017 - 300 = 717 \quad \text{(not possible)} \]

5. If \(x = 20\): \[ y \geq 1017 - 12 \times 20 = 1017 - 240 = 777 \quad \text{(not possible)} \]

Through this exhaustive search, you will find the combination of \(x\) and \(y\) that still lets the scores be achievable. If the results steer towards impossibility, it would denote needing higher marks would thus indicate needing consistent excellent scores on the remaining tests and quizzes to catch up.

The simplest approach would be to obtain the best scores on both tests and the third quiz. Any score less will necessitate exponentially better scores to balance compensations. If negative insights indicate failing, one should consider thoroughly re-evaluating study and preparation methods before tests.