The price, t, of a lawn mower at Turf Cutters is $290 less than three times the price, d, of the same lawn mower at Lawn Masters. The difference in price between the mower at Turf Cutters and Lawn Masters is $240. Which system of equations can be used to determine the price of the mower at each store?
 A. 
t - 3d = -290
t - d = -240

 B. 
3t - 3d = 290
t + d = 240

 C. 
t - 3d = -290
t - d = 240

 D. 
3t - d = 290
t - d = -240



We are given two pieces of information in the problem:

1. The price, $ t $, of a lawn mower at Turf Cutters is $290 less than three times the price, $ d $, of the same lawn mower at Lawn Masters.
2. The difference in price between the lawn mower at Turf Cutters and Lawn Masters is $240.

Let's translate this information into mathematical equations.

### Step 1: Formulating the first equation
- **The price at Turf Cutters is $290 less than three times the price at Lawn Masters**:
  
  This means:
  \[
  t = 3d - 290
  \]
  Rearranging, this becomes:
  \[
  t - 3d = -290
  \]

### Step 2: Formulating the second equation
- **The difference in price between Turf Cutters and Lawn Masters is $240**:
  
  This means:
  \[
  t - d = 240
  \]

### Step 3: Conclusion
So, the system of equations that models this situation is:
\[
\begin{aligned}
t - 3d &= -290 \\
t - d &= 240
\end{aligned}
\]

This corresponds to **Option C**.

Would you like more details or have any questions? Here are 5 related questions:

1. How do you solve this system of equations for $ t $ and $ d $?
2. What method can be used to check if the solution is correct?
3. What is substitution in solving systems of equations?
4. How can you interpret the solution of this system in real life?
5. Can we use graphing to solve this system?

**Tip**: When translating word problems into equations, carefully consider the relationships between quantities, especially terms like "less than" or "times."

The price, t, of a lawn mower at Turf Cutters is $290 less than three times the price, d, of the same lawn mower at Lawn Masters. The difference in price between the mower at Turf Cutters and Lawn Masters is $240. Which system of equations can be used to determine the price of the mower at each store?

Learn how to solve a system of equations to determine the price of a lawn mower at Turf Cutters and Lawn Masters. This problem explores algebraic concepts related to systems of linear equations, focusing on translating word problems into mathematical models. Suitable for students in Grades 8-10.

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