Question

If a = 2b and b = c/4, then a =

• A. 8c
• B. 2c
• C. c
• D. c/2
• E. c/8

Hint:

When you have a chain of relationships like this (a in terms of b, b in terms of c), simply substitute one into the other to find the direct relationship between the first and last variables.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The question asks to express the variable \(a\) in terms of \(c\) by using the given relationships between \(a, b,\) and \(c\). This is a substitution problem.
Step 2: Key Formula or Approach:
We have two equations:
Equation (1): \(a = 2b\)
Equation (2): \(b = c/4\)
Substitute the expression for \(b\) from Equation (2) into Equation (1).
Step 3: Detailed Explanation:
Start with the first equation:
\[ a = 2b \]
Now, replace \(b\) with its equivalent expression from the second equation, which is \(c/4\):
\[ a = 2 \times \left(\frac{c}{4}\right) \]
Multiply the terms:
\[ a = \frac{2c}{4} \]
Simplify the fraction by dividing both the numerator and the denominator by 2:
\[ a = \frac{c}{2} \]
Step 4: Final Answer:
The value of \(a\) in terms of \(c\) is \(c/2\), which corresponds to option (D).