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

To find the weight of Evelyn, let's define the weights of Mr. Adam, Samuel, and Evelyn as follows:

- Let \( S \) be the weight of Samuel.
- Since Mr. Adam is twice as heavy as Samuel, his weight is \( 2S \).
- Since Evelyn is twice as heavy as Mr. Adam, her weight is \( 2 \times 2S = 4S \).

According to the problem, the mean weight of Mr. Adam, his daughter Evelyn, and son Samuel is 14 kg. The mean is given by the total weight divided by the number of people, which is 3. Therefore, we can write the equation:

\[
\frac{S + 2S + 4S}{3} = 14
\]

Simplifying the numerator:

\[
\frac{7S}{3} = 14
\]

To solve for \( S \), multiply both sides of the equation by 3:

\[
7S = 42
\]

Now, divide both sides by 7:

\[
S = 6
\]

We now know that Samuel's weight \( S \) is 6 kg. To find Evelyn's weight, which is \( 4S \):

\[
4S = 4 \times 6 = 24
\]

Thus, the weight of Evelyn is 24 kg.

The correct answer is:

b. 24kg

Would you like any further details or have any questions?

Here are 5 more questions you might consider asking:

1. How do you calculate the mean of a set of numbers?
2. Can you explain how to solve a system of linear equations?
3. What are some real-life applications of mean and average?
4. How do you determine the median and mode of a dataset?
5. Can you demonstrate solving a word problem involving proportions?

**Tip:** When solving word problems, clearly define your variables and translate the given information into equations to simplify the solution process.

Learn how to calculate Evelyn's weight using the mean of Mr. Adam, his daughter Evelyn, and son Samuel, and proportions. This problem involves understanding the relationship between their weights and solving for Evelyn's weight based on given proportions. Suitable for students in Grades 6-8.

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