If one half of one integer is subtracted from three fifths of the next consecutive integer, the difference is 3. What are the two integers?

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To solve this problem, let's break it down step by step:

Step 1: Assign variables
Let's assign the variables x and x+1 to represent the two consecutive integers. Here, x represents the first integer, and x+1 represents the next consecutive integer.

Step 2: Write an equation
Based on the given information, we can write an equation for the problem. According to the problem statement, when one-half of x is subtracted from three-fifths of (x+1), the difference is 3. Mathematically, this can be represented as:

3/5 * (x + 1) - 1/2 * x = 3

Step 3: Solve the equation
Now, let's solve the equation to find the values of x and x+1. To do this, we can simplify the equation and isolate x.

Multiplying both sides of the equation by 10 to eliminate the fractions, we have:

6(x + 1) - 5x = 30

Expanding the equation, we get:

6x + 6 - 5x = 30

Combining like terms, we have:

x + 6 = 30

Subtracting 6 from both sides of the equation, we get:

x = 30 - 6
x = 24

So, the first integer is 24.

Step 4: Find the next consecutive integer
To find the next consecutive integer, we add 1 to the value of x:

x + 1 = 24 + 1
x + 1 = 25

So, the next consecutive integer is 25.

Therefore, the two integers are 24 and 25.