Final answer:
The two numbers that add up to 30 and multiply to get 67.5 are 22.5 and 7.5. These numbers can be found by setting up a system of equations and using the quadratic formula to solve for the values.
Step-by-step explanation:
We are looking to find two numbers that add up to 30 and multiply to get 67.5. This is a classic problem that can be approached using a system of equations. Let's call the two numbers x and y. We can set up the following equations based on the information given:
- x + y = 30 (sum of the two numbers)
- x * y = 67.5 (product of the two numbers)
To solve for x and y, we can use substitution or elimination methods. First, from the equation x + y = 30, we can express y in terms of x as y = 30 - x. Now, we substitute this into the second equation:
x * (30 - x) = 67.5
Expanding the equation we get:
x * 30 - x^2 = 67.5
Bringing all terms to one side:
x^2 - 30x + 67.5 = 0
Now, we can use the quadratic formula to find the values of x. The quadratic formula is:
x = √(b^2 - 4ac)/2a
In our case, a = 1,
b = -30, and
c = 67.5.
After calculation, we find that the two numbers that satisfy both conditions are:
x = 22.5 and y = 7.5, or vice versa.