 Travis bought the same number of tennis rackets and tennis balls. The total cost of 3 tennis rackets and 2 tennis balls was $58. The total cost of 2 tennis rackets and 3 tennis balls was $42. He spent a total of $140 how many tennis balls did travis buy?

Let's define:
- $ r $ as the cost of one tennis racket.
- $ b $ as the cost of one tennis ball.
- $ n $ as the number of tennis rackets and tennis balls Travis bought.

We are given the following information:
1. The total cost of 3 tennis rackets and 2 tennis balls was $58.
    \[
    3r + 2b = 58
    \]
2. The total cost of 2 tennis rackets and 3 tennis balls was $42.
    \[
    2r + 3b = 42
    \]
3. Travis spent a total of $140, and he bought the same number of rackets and balls. So, the total cost for $ n $ rackets and $ n $ balls was $140:
    \[
    n(r + b) = 140
    \]

We first need to solve the system of equations to find $ r $ and $ b $.

### Step 1: Solving the system of equations

We have:
1. $ 3r + 2b = 58 $
2. $ 2r + 3b = 42 $

Multiply the first equation by 3 and the second by 2 to eliminate one variable:
\[
9r + 6b = 174
\]
\[
4r + 6b = 84
\]

Subtract the second equation from the first:
\[
(9r + 6b) - (4r + 6b) = 174 - 84
\]
\[
5r = 90
\]
\[
r = 18
\]

### Step 2: Substituting $ r = 18 $ into one of the original equations

Substitute $ r = 18 $ into $ 2r + 3b = 42 $:
\[
2(18) + 3b = 42
\]
\[
36 + 3b = 42
\]
\[
3b = 6
\]
\[
b = 2
\]

### Step 3: Finding $ n $

Now that we know the cost of a racket ($ r = 18 $) and a ball ($ b = 2 $), we can use the total cost equation:
\[
n(r + b) = 140
\]
\[
n(18 + 2) = 140
\]
\[
n(20) = 140
\]
\[
n = 7
\]

### Final Answer: 
Travis bought **7 tennis balls**.

Would you like further clarification or a more detailed breakdown of any step?

Here are 5 related questions to expand your understanding:
1. How would the total cost change if the price of a tennis racket increased by 10%?
2. If Travis had bought 2 more tennis rackets than tennis balls, how would the total cost equation change?
3. Can we solve this problem using a matrix method? How would it be set up?
4. What if the cost of tennis balls increased to $3, how many could he afford for the same $140 total?
5. What are the other methods to solve two-variable linear equations like this?

**Tip:** When solving systems of equations, try substitution or elimination based on which simplifies the process most quickly.

Travis bought the same number of tennis rackets and tennis balls. The total cost of 3 tennis rackets and 2 tennis balls was $58. The total cost of 2 tennis rackets and 3 tennis balls was $42. He spent a total of $140. How many tennis balls did Travis buy?

Learn how to solve a system of linear equations to determine how many tennis balls Travis bought. Given the total cost of rackets and balls, use algebraic methods to solve this problem. Ideal for students in Grades 8-10.

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