The average age of the groom at a first marriage for a given age of the bride can be approximated by the model y=-.107x^2+5.68x-48.5, 20<=x<=25. Where y is the age of the groom and x is the age of the bride. For what age of the bride is the average age of the groom 26?
What a silly silly question, anyway....
-.107x^2 + 5.68x - 48.5 = 26
-.107x^2 + 5.68x - 74.5 = 0
times 1000 to get rid of all those decimals
107x^2 - 5680x + 74500 = 0
use the quadratic formula and reject any answer that falls outside the given domain
(I did get a valid answer)
To find the age of the bride when the average age of the groom is 26, we need to solve the given equation y = -.107x^2 + 5.68x - 48.5 for x.
Given: y = 26
Substituting y = 26 into the equation, we get:
26 = -.107x^2 + 5.68x - 48.5
This is a quadratic equation. To solve it, we can rearrange the equation and set it equal to zero:
-.107x^2 + 5.68x - 48.5 - 26 = 0
Simplifying further:
-.107x^2 + 5.68x - 74.5 = 0
Now we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation: a = -.107, b = 5.68, c = -74.5
Plugging in these values, we get:
x = (-(5.68) ± √((5.68)^2 - 4*(-.107)*(-74.5))) / (2*(-.107))
Calculating this expression will give us two values of x. We can disregard any values of x that fall outside the given range of 20 <= x <= 25, as mentioned in the problem.
The resulting value(s) of x within the given range will give us the age(s) of the bride where the average age of the groom is 26.