To solve this problem, we need to determine the value of x, which represents the initial amount of food supplies for the journey.
Let's break down the information given:
Initial amount of food supplies: x pounds
Amount of supplies used after one day: 2/5 * x pounds
Amount of supplies remaining after one day: x - (2/5 * x) pounds
Amount of supplies used after two more days: 3/5 * (x - (2/5 * x)) pounds
Amount of supplies remaining after two more days: (x - (2/5 * x)) - (3/5 * (x - (2/5 * x))) pounds
Amount of supplies remaining until they dock: 96 pounds
We can set up the equation as follows:
(x - (2/5 * x)) - (3/5 * (x - (2/5 * x))) = 96
Let's simplify and solve for x:
(x - (2/5 * x)) - (3/5 * (x - (2/5 * x))) = 96
(x - (2/5 * x)) - (3/5 * (3/5 * x)) = 96
(x - (2/5 * x)) - (9/25 * x) = 96
To simplify further, let's find a common denominator for (2/5 * x) and (9/25 * x):
Common denominator = 25
(25/25 * x - 10/25 * x) - (9/25 * x) = 96
(15/25 * x) - (9/25 * x) = 96
(6/25 * x) = 96
To isolate x, we divide both sides of the equation by 6/25:
(6/25 * x) / (6/25) = 96 / (6/25)
x = 96 / (6/25)
To divide by a fraction, we multiply by its reciprocal:
x = 96 * (25/6)
x = 400
The value of x is 400.
#### 400
The answer is: 400
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
A ship left a port and headed due west, having x pounds of food for the journey's supply. After one day of sailing, 2/5 of the supplies had been used by the sailors in the ship. After another two days of sailing, the sailors used 3/5 of the remaining supplies. Calculate the number of supplies remaining in the ship to last the sailors until they dock. The answer is 96.

### Answer:
