To find out what score Ruben needs on his next test to raise his average to 81, we can use the formula for the mean (average):

$\text{Mean} = \frac{\text{Sum of all scores}}{\text{Number of scores}}$

Step 1: Determine the sum of Ruben's current scores.

Ruben's mean score after 6 tests is 79. Therefore, the total sum of his current scores is:

$\text{Sum of current scores} = 79 \times 6 = 474$

Step 2: Determine the sum of scores needed for a new mean of 81 after 7 tests.

To have an average of 81 after 7 tests, the sum of all his scores must be:

$\text{Sum needed} = 81 \times 7 = 567$

Step 3: Determine the score needed on the next test.

The score Ruben needs on his next test can be found by subtracting the sum of his current scores from the sum needed:

$\text{Next score} = 567 - 474 = 93$

Conclusion:

Ruben needs to score 93 on his next test to raise his average to 81.

Would you like more details or have any questions?

Here are five related questions for further practice:

1. What if Ruben wants to raise his average to 85 instead of 81?
2. How would the required score change if Ruben had only taken 5 tests so far?
3. What would his new average be if he scores 100 on the next test?
4. What score would he need on the next test to maintain an average of 79?
5. How many more tests would he need to take if he wants to raise his average to 81 without scoring 93?

Tip: Always check the number of total tests when calculating averages, as it directly impacts the required score.