Final answer:
To solve this problem, we need to set up two equations based on the given information and then solve for the two numbers. Let x be the first number and y be the second number. Using the equations x + y = 12 and 3x - 9 = y - 1, we can find that x is approximately 5.25 and y is approximately 6.75.
Step-by-step explanation:
To solve this problem, we need to set up two equations based on the given information and then solve for the two numbers.
Let's say the two numbers are x and y.
We are given that the sum of the two numbers is 12, so we can write the equation x + y = 12.
We are also given that nine less than three times the first number is one less than the second number, so we can write the equation 3x - 9 = y - 1.
Now we can solve these two equations simultaneously to find the values of x and y.
Substitute the value of y in the first equation with the expression 3x - 9 in the second equation: x + (3x - 9) = 12.
Simplify the equation: 4x - 9 = 12.
Add 9 to both sides of the equation: 4x = 21.
Divide both sides of the equation by 4: x = 5.25.
Substitute the value of x into the first equation to solve for y: 5.25 + y = 12.
Subtract 5.25 from both sides of the equation: y = 6.75.
Therefore, the two numbers are approximately 5.25 and 6.75.