 If your scores in the first three tests are 82, 89, and 78, what must your score in the fourth test in order to obtain an average of 85?

To find the score you need on the fourth test to achieve an average of 85, we can set up an equation. Let's denote your fourth test score as \( x \).

The average of four test scores is given by the formula:

\[
\text{Average} = \frac{\text{Sum of all test scores}}{\text{Number of tests}}
\]

We know:
- Your first three test scores: 82, 89, and 78
- You want an average of 85 over four tests.

So, we set up the equation:

\[
\frac{82 + 89 + 78 + x}{4} = 85
\]

First, add the scores from the first three tests:

\[
82 + 89 + 78 = 249
\]

Now, substitute into the equation:

\[
\frac{249 + x}{4} = 85
\]

Next, multiply both sides of the equation by 4 to eliminate the fraction:

\[
249 + x = 340
\]

Finally, solve for \( x \):

\[
x = 340 - 249 = 91
\]

So, you must score **91** on the fourth test to achieve an average of 85.

Would you like more details or have any further questions?

Here are 8 related questions:
1. How is the required score affected if you want an average of 90 instead of 85?
2. What would be your average if you scored 85 on the fourth test?
3. How do you calculate the average if you have a different number of tests?
4. If the fourth test score was lower, say 75, what would your new average be?
5. How does dropping the lowest score affect your average?
6. What if there were 5 tests and you still wanted an average of 85?
7. Can you achieve an average of 85 if your highest possible score is 90?
8. How would an average change if all test scores were increased by 5 points?

**Tip:** When working with averages, setting up an equation based on the sum of all values is often the easiest way to find the unknown value.

Find out how to calculate your score on the fourth test to achieve an average of 85. Learn the step-by-step method using the average formula and solve the equation with examples. Suitable for Grades 7-9 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation