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We have been given that during one period extreme cold, the average daily temperature decreased degree F each day. We are asked to find number of days it will take for the temperature to decrease by 9 degree F.
First of all we will convert our mixed fraction into improper fraction.
Now we will divide total temperature change (9) by average daily temperature change () to find number of days.
Dividing a number by a fraction is same as multiplying the number by reciprocal of the fraction.
Therefore, it will take 6 days for the temperature to decrease by 9 degree F.
Given
We have to set the restraint
because a square root is non-negative, and thus it can't equal a negative number. With this in mind, we can square both sides:
The solutions to this equation are 7 and -2. Recalling that we can only accept solutions greater than or equal to -1, 7 is a feasible solution, while -2 is extraneous.
Similarly, we have
So, we have to impose
Squaring both sides, we have
The solutions to this equation are 5 and 10. Since we only accept solutions greater than or equal to 7, 10 is a feasible solution, while 5 is extraneous.