In a contest , 2 participants were asked about their age . To test the strength of their math , they are asked to add their ages together. One answer 44 and the other gives 1280. The first obtained from the parse age with one another , while the second can multiply both their age . How old are they ?
If I interpreted the rather garbled English, you want x and y where
x+y = 44
xy = 1280
To solve this problem, we need to set up a system of equations using the given information.
Let's assume the ages of the two participants are represented by variables:
Participant 1's age = x
Participant 2's age = y
According to the information provided, we have:
Equation 1: x + y = 44 (because the first participant added their ages)
Equation 2: x * y = 1280 (because the second participant multiplied their ages)
Now we can solve these equations simultaneously to find the values of x and y.
There are various methods to solve this system of equations, but let's use the substitution method.
From Equation 1, we can express x in terms of y:
x = 44 - y
Substituting this value of x in Equation 2:
(44 - y) * y = 1280
44y - y^2 = 1280
Rearranging the equation to a quadratic form:
y^2 - 44y + 1280 = 0
We can factorize or use the quadratic formula to solve this equation. Factoring may not be possible in this case, so let's use the quadratic formula:
y = (-b ± √(b^2 - 4ac)) / 2a
Plugging in the values:
y = (-(-44) ± √((-44)^2 - 4 * 1 * 1280)) / (2 * 1)
y = (44 ± √(1936 - 5120)) / 2
y = (44 ± √(-3184)) / 2
Since the square root of a negative number is not possible in real numbers, we can conclude that there is no real solution to this equation. It means there is no combination of ages that can satisfy both equations simultaneously.
Therefore, there may be an error or inconsistency within the given information.