Answer:
or 
Step-by-step explanation:
Use 45-45-90 triangle theorem
3*
We're minimizing

subject to

. Using Lagrange multipliers, we have the Lagrangian

with partial derivatives

Set each partial derivative equal to 0:

Subtracting the second equation from the first, we find

Similarly, we can determine that

and

by taking any two of the first three equations. So if

determines a critical point, then

So the smallest value for the sum of squares is

when

.
It has been given that y varies inversely with x, therefore the equation for this relationship is as follows;
y =

\
when y = -18 and x = 6
-18 = k/ 6 ---1)
We need to find x when y = 5
5 = k/x
when we divide 1)/2), k gets cancelled

x = -18*6/5
x = -21.6
when y = 5, then x = -21.6
Since Bryan spent $15.50 less than Sarah, you would start by dividing the total amount they spent together in half.
$47.50 ÷ 2 = $23.75
Then you would take Bryan's 1/2 of the total and subtract $15.50.
$23.75 - $15.50 = $8.25
So, it looks like Bryan spent $8.25.
Check step:
If you add it all back together:
Sarah + Sarah Bryan = Total
$23.75 + $15.50 + $8.25 = $47.50