Question

If a = 2b and b = 3c, what is the value of a when c = 4?

• A. 6
• B. 9
• C. 10
• D. 20
• E. 24

Hint:

When variables are linked in a simple chain (\(a \rightarrow b \rightarrow c\)), you can find the relationship between the first and last variable by multiplying their coefficients. Here, \(a = (2 \times 3)c = 6c\).

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
This is a substitution problem where the value of one variable is used to find the next in a sequence until the final target variable is found.
Step 2: Key Formula or Approach:
We can solve this in two ways: by sequentially calculating the value of each variable, or by first creating a direct formula for \(a\) in terms of \(c\).
Step 3: Detailed Explanation:
Method 1: Sequential Calculation
We are given that \(c = 4\).
First, we find the value of \(b\) using the equation \(b = 3c\):
\[ b = 3 \times 4 = 12 \]
Now we use the value of \(b\) to find \(a\) using the equation \(a = 2b\):
\[ a = 2 \times 12 = 24 \]
Method 2: Substitution
We have \(a = 2b\) and \(b = 3c\). Substitute the expression for \(b\) into the first equation:
\[ a = 2(3c) = 6c \]
Now we have a direct relationship between \(a\) and \(c\). We can substitute \(c = 4\):
\[ a = 6 \times 4 = 24 \]
Step 4: Final Answer:
The value of \(a\) is 24, which corresponds to option (E).