Final answer:
To find the smallest values for the integers, we can set up equations based on the given information and solve for the values of the integers.
Step-by-step explanation:
To find the smallest values for the integers, let's assume one integer is represented by x and the other by y.
We are given that one integer is 3 more than twice the other. So we can set up the equation x = 2y + 3.
The sum of the integers is greater than 24, so x + y > 24.
Now, we need to find the smallest values that satisfy both equations. Let's start by substituting the value of x from the first equation into the second equation:
2y + 3 + y > 24
Combining like terms, we get 3y + 3 > 24.
Subtracting 3 from both sides, we have 3y > 21.
Finally, dividing both sides by 3, we find y > 7.
Since y must be an integer, the smallest possible value for y is 8.
Substituting this value back into the first equation, we have x = 2(8) + 3, which gives x = 19.
Therefore, the smallest values for the integers are y = 8 and x = 19.