To solve this problem, we need to determine the value of x, which represents the cost of buying a replacement stove.
Let's break down the information given:
Cost of buying a replacement stove: x
Cost of fixing the wall: 1/6 * x
Total cost: $1400
We can set up the equation as follows:
Cost of buying a replacement stove + Cost of fixing the wall = Total cost
x + 1/6 * x = $1400
Let's simplify and solve for x:
1 * x + 1/6 * x = $1400
To simplify the equation, we need to find a common denominator for 1 and 1/6, which is 6:
6/6 * x + 1/6 * x = $1400
6/6 * x + 1/6 * x = $1400
(6 + 1)/6 * x = $1400
7/6 * x = $1400
To isolate x, we multiply both sides of the equation by 6/7:
(6/7 * 7/6) * x = $1400 * 6/7
x = $1200
The value of x is $1200.
#### 1200
The answer is: 1200
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Jason's stove catches on fire. Buying a replacement will cost $x and fixing the damage to the wall behind it will cost 1/6th as much. He spends 1400 in total.

### Answer:
