Given that XY =21 and 1 < x < 2, find the sum of the upper and lower bounds of Y. Express your answer as a decimal.
To find the sum of the upper and lower bounds of Y, we first need to determine the possible values for Y by considering the range of X.
We are given that XY = 21. Let's rewrite this equation as: Y = 21/X.
The bounds for X are given as 1 < x < 2. Since X cannot be equal to 0, we can't have infinitely small values for Y. Therefore, we need to find the upper and lower bounds of Y within the given range for X.
To find the upper and lower bounds of Y, we substitute the lower bound (x = 1) and the upper bound (x = 2) into the equation Y = 21/X:
For the lower bound of X:
Y_lower = 21/1 = 21
For the upper bound of X:
Y_upper = 21/2 = 10.5
The sum of the upper and lower bounds of Y is given by:
Y_lower + Y_upper = 21 + 10.5 = 31.5
Therefore, the sum of the upper and lower bounds of Y is 31.5.