Tony has an A average in his math class and there is one test left. In order to keep the A, he will have to maintain an average test score that is at least 90%. He has completed 5 of the 6 tests and his current average is 91%.Which fo the following scores is th elowest he can earn while still maintaining his A ?

Options

A. 0.8
B. 0.85
C. 0.89
D. 0.9

Answer

To solve the problem step by step, we will follow these calculations:

1. **Understanding the Problem**: Tony has completed 5 tests with an average score of 91%. He needs to maintain an average of at least 90% after taking one more test.

2. **Calculating the Total Score for the First 5 Tests**:
- The average score of the first 5 tests is given as 91%.
- The formula for average is:
\[ \text{Average} = \frac{\text{Sum of scores}}{\text{Number of tests}} \]
- Let \( S_5 \) be the sum of the scores of the first 5 tests. Then:
\[ 91 = \frac{S_5}{5} \]
- Rearranging gives:
\[ S_5 = 91 \times 5 = 455 \]

3. **Setting Up the Equation for the Average After 6 Tests**:
- Let \( X \) be the score Tony needs on the 6th test.
- The average score after 6 tests must be at least 90%. Therefore:
\[ \text{Average after 6 tests} = \frac{S_5 + X}{6} \geq 90 \]
- Substituting \( S_5 \) into the equation:
\[ \frac{455 + X}{6} \geq 90 \]

4. **Solving the Inequality**:
- Multiply both sides by 6 to eliminate the fraction:
\[ 455 + X \geq 540 \]
- Now, isolate \( X \):
\[ X \geq 540 - 455 \]
- Simplifying gives:
\[ X \geq 85 \]

5. **Conclusion**:
- The lowest score Tony can earn on the 6th test while still maintaining his A average is **85**.

### Summary of Steps:
1. Calculate the total score of the first 5 tests using the average.
2. Set up an equation for the average after 6 tests.
3. Solve the inequality to find the minimum score needed on the last test.