The mean weight of Mr. Adam, his daughter Evelyn and son Samuel is 14kg. If it is known that Mr. Adam is twice as heavy as Samuel and Evelyn is twice as heavy as Mr. Adam, what is the weight of Evelyn?Question 12Answer
a.
8kg
b.
24kg
c.
4kg
d.
12kg

Given the mean weight of Mr. Adam, his daughter Evelyn, and his son Samuel is 14 kg, we can set up the following equation for their total weight:

\[ \frac{W_A + W_E + W_S}{3} = 14 \]

where \( W_A \), \( W_E \), and \( W_S \) represent the weights of Mr. Adam, Evelyn, and Samuel, respectively.

First, we find their total weight:

\[ W_A + W_E + W_S = 14 \times 3 = 42 \]

Next, we use the given information about their weights:

1. Mr. Adam is twice as heavy as Samuel:
\[ W_A = 2W_S \]

2. Evelyn is twice as heavy as Mr. Adam:
\[ W_E = 2W_A \]

Substitute \( W_A \) from the first equation into the second equation:

\[ W_E = 2(2W_S) = 4W_S \]

Now, substitute \( W_A \) and \( W_E \) in terms of \( W_S \) into the total weight equation:

\[ 2W_S + 4W_S + W_S = 42 \]

Combine like terms:

\[ 7W_S = 42 \]

Solve for \( W_S \):

\[ W_S = \frac{42}{7} = 6 \]

Now, find \( W_A \):

\[ W_A = 2W_S = 2 \times 6 = 12 \]

Finally, find \( W_E \):

\[ W_E = 4W_S = 4 \times 6 = 24 \]

Therefore, the weight of Evelyn is:

\[ \boxed{24 \text{ kg}} \]

Answer: (b) 24kg

Do you want any more details or have any questions?

Here are some more questions you might find interesting:

1. How do you calculate the mean of a set of numbers?
2. What are some real-life applications of solving such weight problems?
3. How would the equation change if Mr. Adam was three times as heavy as Samuel?
4. Can you solve a similar problem where the total weight is different?
5. How does understanding these concepts help in fields like physics or engineering?

**Tip:** Always substitute given relationships into the primary equation to reduce the number of variables before solving.

Learn how to solve the weight problem involving Mr. Adam, his daughter Evelyn, and son Samuel with a mean weight of 14 kg. Understand the relationships between their weights using proportions and algebraic equations. Suitable for students in Grades 7-9.

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