Final answer:
The problem is a simple linear equation where one number is 3 more than twice the second number and their sum is 45. By setting the second number as x, the equation 3x + 3 = 45 leads to x = 14. Plugging x into 2x + 3 gives the first number, which is 31.
Step-by-step explanation:
To solve the problem where one number is 3 more than twice the second number, and their sum is 45, let's denote the second number as x. According to the problem, the first number is twice the second number plus 3, so it can be expressed as 2x + 3.
The sum of these two numbers is 45, as given by the problem. So, we can create the following equation to represent the relationship:
x + (2x + 3) = 45
Combining like terms gives us:
3x + 3 = 45
Subtracting 3 from both sides:
3x = 42
Dividing both sides by 3 gives us the value of the second number:
x = 14
Now, to find the first number, we plug the value of x into 2x + 3:
2(14) + 3 = 31
So the second number is 14 and the first number is 31.