The average of r and s is 7.5, and the average of r, s and t is 11. What is the value of t?

Answer

To solve the problem step by step, we will use the information given about the averages of the numbers r, s, and t.

### Step 1: Understand the average of r and s
The average of r and s is given as 7.5. The formula for the average is:

\[ \text{Average} = \frac{\text{Sum of values}}{\text{Number of values}} \]

For r and s, we can write:

\[ \frac{r + s}{2} = 7.5 \]

### Step 2: Calculate the sum of r and s
To find the sum of r and s, we can multiply both sides of the equation by 2:

\[ r + s = 7.5 \times 2 \]

Calculating this gives:

\[ r + s = 15 \]

### Step 3: Understand the average of r, s, and t
Next, we know that the average of r, s, and t is 11. Using the average formula again, we have:

\[ \frac{r + s + t}{3} = 11 \]

### Step 4: Calculate the sum of r, s, and t
To find the sum of r, s, and t, we can multiply both sides of the equation by 3:

\[ r + s + t = 11 \times 3 \]

Calculating this gives:

\[ r + s + t = 33 \]

### Step 5: Substitute the value of r + s
Now we can substitute the value of r + s that we found in Step 2 into this equation:

\[ 15 + t = 33 \]

### Step 6: Solve for t
To find the value of t, we can rearrange the equation:

\[ t = 33 - 15 \]

Calculating this gives:

\[ t = 18 \]

### Final Answer
The value of t is **18**.

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