In a class of 10 boys and 15 girls, the average score on a biology test is 90. If the average score for the girls is x, what is the average score for the boys in terms of x ?

Options

A. `200-(2)/(3)x`
B. `225-(3)/(2)x`
C. `250-2x`
D. `250-3x`

Explanation

To find the average score for the boys in terms of the average score for the girls (x), we can follow these steps:

### Step 1: Understand the given information
We have a class of 10 boys and 15 girls, and the average score for the entire class is 90.

### Step 2: Calculate the total number of students
The total number of students is:
\[ 10 \text{ (boys)} + 15 \text{ (girls)} = 25 \text{ (total students)} \]

### Step 3: Calculate the total score of the class
Using the average score, we can find the total score of the class:
\[ \text{Total score} = \text{Average score} \times \text{Total number of students} = 90 \times 25 = 2250 \]

### Step 4: Express the total score of girls
Let the average score of the girls be \( x \). Therefore, the total score of the girls is:
\[ \text{Total score of girls} = 15 \times x = 15x \]

### Step 5: Express the total score of boys
Let the average score of the boys be \( y \). Therefore, the total score of the boys is:
\[ \text{Total score of boys} = 10 \times y = 10y \]

### Step 6: Set up the equation for total score
The total score of the class is the sum of the total scores of boys and girls:
\[ 15x + 10y = 2250 \]

### Step 7: Solve for \( y \)
Now, we can rearrange the equation to find \( y \):
\[ 10y = 2250 - 15x \]
\[ y = \frac{2250 - 15x}{10} \]
\[ y = 225 - 1.5x \]

### Conclusion
Thus, the average score for the boys in terms of \( x \) is:
\[ y = 225 - 1.5x \]

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