High School

Sam and Hector are gaining weight for football season. Sam weighs 205 pounds and is gaining 2 pounds per week. Hector weighs 195 pounds but is gaining 3 pounds per week.

In how many weeks will they both weigh the same amount?

Answer :

To solve the problem of determining when Sam and Hector will weigh the same amount, we need to compare their weekly weight gains.

1. Initial Weights and Gains:
- Sam starts at 205 pounds and gains 2 pounds every week.
- Hector starts at 195 pounds and gains 3 pounds every week.

2. Set Up the Problem:
- We need to find the number of weeks (let's call it [tex]\( w \)[/tex]) after which both Sam and Hector will weigh the same.

3. Write the Equations:
- For Sam: Weight after [tex]\( w \)[/tex] weeks = [tex]\( 205 + 2w \)[/tex].
- For Hector: Weight after [tex]\( w \)[/tex] weeks = [tex]\( 195 + 3w \)[/tex].

4. Equate the Two Expressions:
- Since we want their weights to be equal, set the two equations equal to each other:
[tex]\[
205 + 2w = 195 + 3w
\][/tex]

5. Solve for [tex]\( w \)[/tex]:
- Simplify the equation:
[tex]\[
205 + 2w = 195 + 3w
\][/tex]
- Subtract [tex]\( 2w \)[/tex] from both sides:
[tex]\[
205 = 195 + w
\][/tex]
- Subtract 195 from both sides:
[tex]\[
10 = w
\][/tex]

6. Conclusion:
- It will take 10 weeks for Sam and Hector to weigh the same.
- At that time, both will weigh 225 pounds.

This step-by-step solution outlines how Sam and Hector will weigh the same amount, which happens after 10 weeks.

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