Question

John weighs twice as much as Maria. Maria's weight is 60% of Bob's weight. Dave's weight is 50% of Lee's. Lee weighs 190% as much as John does. Which of these 5 persons weighs the least?

• A. John
• B. Dave
• C. Maria
• D. Bob

Hint:

To avoid decimals, you can assign a convenient number to the base variable. If Maria = 60 kg, then Bob = 100 kg, John = 120 kg, Lee = 228 kg, and Dave = 114 kg. It's immediately clear Maria is the lightest.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We are given the relative weights of five individuals and need to determine who is the lightest. We can solve this by expressing everyone's weight in terms of a single person's weight.


Step 2: Key Formula or Approach:
Set up linear equations based on the given percentages and ratios, and express all variables in terms of one base variable (e.g., Maria's weight).


Step 3: Detailed Explanation:
Let Maria's weight be represented by \( M \).
1. John (\( J \)) weighs twice as much as Maria:
\[ J = 2M \] 2. Maria's weight is 60% of Bob's (\( B \)) weight:
\[ M = 0.60 \times B \implies B = \frac{M}{0.6} = \frac{10}{6}M \approx 1.67M \] 3. Lee (\( L \)) weighs 190% as much as John does:
\[ L = 1.90 \times J = 1.90 \times (2M) = 3.8M \] 4. Dave (\( D \))'s weight is 50% of Lee's:
\[ D = 0.50 \times L = 0.50 \times (3.8M) = 1.9M \] Now, let's compare all weights in terms of \( M \):
Maria = \( 1M \)
John = \( 2M \)
Bob = \( \approx 1.67M \)
Lee = \( 3.8M \)
Dave = \( 1.9M \)
Comparing the coefficients, 1 is the smallest. Therefore, Maria weighs the least.


Step 4: Final Answer:
Maria is the person who weighs the least.