To determine the minimum score Myra needs on her last test to have an average greater than 90, let's solve this step by step.

Given Scores:

84, 99, 88, 82, 95, 85

Let $x$ be the score Myra gets on her last test. She has 7 tests total (6 scores given + 1 final test score).

Step 1: Express the Average

To have an average greater than 90, the total score divided by 7 must be greater than 90. Mathematically:

$\frac{\text{sum of all scores}}{7} > 90$

Rearranging:

$\text{sum of all scores} > 90 \times 7 = 630$

Step 2: Find the Sum of the 6 Given Scores

The sum of Myra's scores is:

$84 + 99 + 88 + 82 + 95 + 85 = 533$

Step 3: Solve for $x$ (Minimum Score Needed)

Adding the final test score $x$, the total sum becomes:

$533 + x > 630$

Simplifying for $x$:

$x > 630 - 533$ $x > 97$

Step 4: Conclusion

The minimum score Myra can make on her last test to have an average greater than 90 is:

$\boxed{98}$

Verification:

If Myra scores 98: $\text{Total Score} = 533 + 98 = 631$ $\text{Average} = \frac{631}{7} = 90.14 > 90$

Thus, a score of 98 ensures the average is greater than 90.

Would you like a more detailed explanation or verification with similar examples? Let me know!

Related Questions:

1. How do you calculate the average of a dataset?
2. What is the difference between "greater than" and "greater than or equal to" in inequalities?
3. How do you determine the minimum or maximum value needed to meet a condition?
4. Can you explain step-by-step how to solve similar word problems with averages?
5. How would the solution change if Myra's target average was 95 instead of 90?

Tip:

To check averages quickly, always multiply the target average by the total number of items, then adjust for missing or known values.