The​ average, or​ mean, Upper T​, of three exam​ grades, y​, r​, and w​, is given by the following formula.
Upper T equals StartFraction y plus r plus w Over 3 EndFraction
​(a) Solve the formula for w.
​(b) Use the formula in part​ (a) to solve this problem. On your first two​ exams, your grades are 85​% and 87​%: yequals85 and requals87. What must you get on the third exam to have an average of 87​%?
Question content area bottom
Part 1
​(a) The formula is wequals

enter your response here.

Let's go through each part of the problem step by step.

### Part (a) - Solve the formula for \( w \):

The average \( T \) of three exam grades \( y \), \( r \), and \( w \) is given by the formula:
\[
T = \frac{y + r + w}{3}
\]
To solve for \( w \), follow these steps:

1. Multiply both sides by 3 to eliminate the denominator:
\[
3T = y + r + w
\]

2. Subtract \( y + r \) from both sides to isolate \( w \):
\[
w = 3T - y - r
\]

So, the formula solved for \( w \) is:
\[
w = 3T - y - r
\]

### Part (b) - Calculate the required grade on the third exam:

You are given the grades for the first two exams, \( y = 85\% \) and \( r = 87\% \), and you need to find the grade \( w \) on the third exam that would result in an average of \( T = 87\% \).

Using the formula derived in part (a):
\[
w = 3T - y - r
\]

Substitute the known values:
\[
w = 3(87) - 85 - 87
\]

Now, let's calculate the value of \( w \):
\[
w = 261 - 85 - 87 = 261 - 172 = 89
\]

So, you need to score **89%** on the third exam to achieve an average of 87%.

---

Would you like any further details or explanations on these steps?

### Related Questions:
1. What would the grade \( w \) be if the target average \( T \) was 90% instead of 87%?
2. How would the result change if your grades were 85%, 88%, and you aimed for an average of 87%?
3. If you got an 89% on the third exam, what would your new average be?
4. How does changing one of the initial grades \( y \) or \( r \) affect the required grade \( w \)?
5. What is the minimum grade you could get on the third exam to still achieve at least an 85% average?

### Tip:
When solving equations, always perform the same operation on both sides to maintain equality.

Learn how to solve an average problem with exam grades using a step-by-step solution approach. Calculate the required grade on the third exam to achieve an average of 87% given initial grades of 85% and 87%. Suitable for high school 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