Final answer:
To solve the problem, we translate the given scenario into a set of algebraic equations and then solve for the variables. We find that the two numbers are 2 and 5.
Step-by-step explanation:
The problem states that one number is three less than four times another number and that the sum of these numbers is 7. This situation can be translated into two algebraic equations.
Let's denote the first number as x and the second number as y. According to the problem, we can express y in terms of x as y = 4x - 3. Furthermore, we know that their sum is 7, so we have the equation x + y = 7.
To find the numbers, we substitute y in the second equation with the expression from the first equation:
x + (4x - 3) = 7.
Combining like terms, we have:
5x - 3 = 7.
Adding 3 to both sides gives us:
5x = 10.
Dividing both sides by 5 we get:
x = 2.
Now we can find y by substituting x back into the first equation:
y = 4(2) - 3
Which simplifies to:
y = 8 - 3 = 5.
Therefore, the two numbers are 2 and 5.