Final answer:
To solve the student's question, the smallest consecutive integer was denoted as x; an equation was set up based on the given relationship and solved to find that the three consecutive integers are 2, 3, and 4.
Step-by-step explanation:
This problem involves solving an equation that describes the relationships between three consecutive integers. Let's denote the smallest integer as x. The next consecutive integer would be x + 1, and the one after that would be x + 2. The sum of these three integers can be expressed as x + (x + 1) + (x + 2). According to the given condition, this sum is equal to twice the smallest increased by 5, which translates to the equation 2x + 5.
Formulating the Equation
We then set up the equation based on the described relationship:
x + (x + 1) + (x + 2) = 2x + 5
Combining like terms on the left side gives us:
3x + 3 = 2x + 5
Subtracting 2x from both sides, we have:
x + 3 = 5
And, subtracting 3 from both sides yields:
x = 2
So, the smallest consecutive integer is 2, which means the three consecutive integers are 2, 3, and 4.