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.