The sum of two numbers is 3. Four times the larger number plus three times the smaller number is 25. Find the numbers.

The larger number is___?
and the smaller number is___?

3x + 4(3-x) = 25

To solve this problem, let's assign variables to both numbers. Let's call the larger number "x" and the smaller number "y".

From the given information, we know that the sum of the two numbers is 3. This can be expressed by the equation:

x + y = 3 (Equation 1)

We are also given that four times the larger number plus three times the smaller number is 25. This can be expressed by the equation:

4x + 3y = 25 (Equation 2)

Now, we have a system of two equations with two variables. We can solve this system using the method of substitution or elimination.

Let's use the method of substitution to find the solution:

From Equation 1, we can express y in terms of x:

y = 3 - x

We can substitute this expression for y in Equation 2:

4x + 3(3 - x) = 25

Simplifying the equation:

4x + 9 - 3x = 25

Combining like terms:

x + 9 = 25

Subtracting 9 from both sides:

x = 16

Now that we have the value of x, we can substitute it back into Equation 1 to find y:

16 + y = 3

Subtracting 16 from both sides:

y = -13

So, the larger number is 16 and the smaller number is -13.