Team one has twice as many workers as team two. Because of increased productivity, the number of
workers on team one is reduced by 5, and the number of workers on team two is reduced by 2. How many
workers are on each team now if there are 7 more workers on team one than on team two?

Let \( x \) represent the number of workers originally on team two. Since team one has twice as many workers as team two, the original number of workers on team one is \( 2x \).

After the reductions, the number of workers on team one becomes \( 2x - 5 \), and the number of workers on team two becomes \( x - 2 \).

We are told that there are now 7 more workers on team one than on team two, which gives the equation:
\[
2x - 5 = (x - 2) + 7
\]

### Solve the equation:
1. Expand the right-hand side:
   \[
   2x - 5 = x - 2 + 7
   \]
   \[
   2x - 5 = x + 5
   \]

2. Subtract \( x \) from both sides:
   \[
   2x - x - 5 = 5
   \]
   \[
   x - 5 = 5
   \]

3. Add 5 to both sides:
   \[
   x = 10
   \]

Now that we know \( x = 10 \), the original number of workers on team two was 10, and the original number of workers on team one was \( 2x = 20 \).

After the reductions:
- Team one now has \( 20 - 5 = 15 \) workers.
- Team two now has \( 10 - 2 = 8 \) workers.

Thus, team one now has 15 workers, and team two has 8 workers.

Would you like further details or have any questions?

Here are 5 related questions to explore further:
1. What happens if the number of workers on both teams is reduced by a different amount?
2. How would the scenario change if team two had originally three times fewer workers than team one?
3. What if instead of reducing workers, both teams were increased by a certain percentage?
4. How can we generalize this approach for any number of teams and reductions?
5. How would the solution change if the number of workers on team two was not given directly?

**Tip:** When solving problems involving comparisons, setting up an equation based on relationships between variables is key to finding the solution easily.

Team one has twice as many workers as team two. Because of increased productivity, the number of workers on team one is reduced by 5, and the number of workers on team two is reduced by 2. How many workers are on each team now if there are 7 more workers on team one than on team two?

Learn how to solve a word problem involving linear equations, where the number of workers on two teams is adjusted due to productivity changes. The problem involves setting up and solving equations to find the current number of workers on each team, suitable for students in Grades 6-8.

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