Question

If \( \frac{a}{b} = \frac{3}{4} \) and b=8, what is a?

• A. 6
• B. 8
• C. 9
• D. 12

Hint:

Another way to solve proportions is by finding the scaling factor. Look at the denominators: to get from 4 to 8, you multiply by 2. To keep the proportion equal, you must do the same to the numerators. So, \( a = 3 \times 2 = 6 \).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This problem involves solving a proportion. We are given a ratio and the value of one of the variables, and we need to find the value of the other.
Step 2: Detailed Explanation:
We are given the equation:
\[ \frac{a}{b} = \frac{3}{4} \] We are also given that \( b = 8 \). Substitute this value into the equation:
\[ \frac{a}{8} = \frac{3}{4} \] To solve for 'a', we can use cross-multiplication:
\[ a \times 4 = 8 \times 3 \] \[ 4a = 24 \] Now, divide both sides by 4 to isolate 'a':
\[ a = \frac{24}{4} \] \[ a = 6 \] Note: The provided answer key in the OCR text says "(D) 6". This appears to be a typo, as option (D) is 12, while the correct numerical answer is 6, which corresponds to option (A). Our calculation confirms the correct answer is 6.
Step 3: Final Answer:
The value of a is 6.