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Let's solve this step by step.

We are given the following information:

- The total cost of a desk and a chair when bought separately is $420.
- The desk costs $300 more than the chair.
- When bought together, there is a 40% discount on the price of the chair.

Let's define:
- $ x $ as the price of the chair.

Then, the price of the desk will be:
- $ x + 300 $.

The total cost of both, when bought separately, is $420. Therefore, we have the equation:
\[
x + (x + 300) = 420
\]
Simplifying this equation:
\[
2x + 300 = 420
\]
\[
2x = 120
\]
\[
x = 60
\]

So, the original price of the chair is $60.

Now, with the 40% discount, the discounted price of the chair is:
\[
0.60 \times 60 = 36
\]

Therefore, the cost of the chair when bought with the discount is **$36**.

Would you like further details on any part of this? Here are some related questions to expand on:

1. How would the problem change if the desk cost twice as much as the chair?
2. How can we check the answer by calculating the price of the desk with this solution?
3. What would be the total discounted price for both items?
4. What is the algebraic method to solve for two unknowns with similar conditions?
5. How can percentages be used in more complex discount scenarios?

**Tip**: Always verify the final answer by checking the original conditions of the problem.

A desk and a chair, if bought separately, would in total cost $420. The desk costs $300 more than the chair. When you buy them together you get 40% off the price of the chair. How much does the chair cost when bought with the discount available with the desk?

Learn how to solve a real-world algebra problem involving the price of a chair and desk, where the desk costs $300 more than the chair, and a 40% discount is applied to the chair when bought together. Step-by-step solution provided, ideal for students in Grades 7-9.

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