David’s mass is 5 kg less than Sucha’s, who in turn  is 8 kg lighter than paul. If their total mass is 197 kg, how heavy is each person?

Let’s solve the problem using algebra. We'll define the masses of the individuals as follows:

- Let \( P \) represent Paul’s mass (in kg).
- Sucha’s mass is \( P - 8 \) kg (since Sucha is 8 kg lighter than Paul).
- David’s mass is \( (P - 8) - 5 = P - 13 \) kg (since David is 5 kg less than Sucha).

Given that their total mass is 197 kg, we can write the equation:
\[
P + (P - 8) + (P - 13) = 197
\]

Simplify the equation:
\[
P + P - 8 + P - 13 = 197
\]
\[
3P - 21 = 197
\]

Now, solve for \( P \):
\[
3P = 197 + 21
\]
\[
3P = 218
\]
\[
P = \frac{218}{3}
\]
\[
P = 72.67 \, \text{kg}
\]

So, Paul's mass is 72.67 kg.

Now let's find the masses of Sucha and David:
- Sucha’s mass = \( P - 8 = 72.67 - 8 = 64.67 \, \text{kg} \)
- David’s mass = \( P - 13 = 72.67 - 13 = 59.67 \, \text{kg} \)

### Answer:
- **Paul’s mass:** 72.67 kg
- **Sucha’s mass:** 64.67 kg
- **David’s mass:** 59.67 kg

Would you like a detailed breakdown of each step, or do you have any questions?

### Related Questions:
1. If Paul's mass was increased by 10 kg, what would their total mass be?
2. What would happen to David's mass if Sucha's mass was doubled?
3. How much heavier is Paul compared to David?
4. What would be their individual masses if their total mass was reduced to 180 kg?
5. If David gains 5 kg, how much would the new total mass be?

### Tip:
When dealing with multiple relationships, always try to express everything in terms of a single variable to simplify the calculations.

David’s mass is 5 kg less than Sucha’s, who in turn is 8 kg lighter than Paul. If their total mass is 197 kg, how heavy is each person?

Discover how to solve a linear equation problem where David, Sucha, and Paul have mass relationships. Paul is the heaviest, Sucha is 8 kg lighter than Paul, and David is 5 kg lighter than Sucha. With a total mass of 197 kg, find their individual masses using algebra. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation