As you can see in the given figure, there are two intersecting chords inside the circle.
Recall that the "Intersecting Chords Theorem" is given by

For the given case, we have
AE = 7
BE = 6
EC = 9
Let us substitute these values into the above equation and solve for DE

Therefore, the length of DE is 10.5 units.
You still want at most
(15x) + (22y) ≤ 100(-z) (equation used)
0 ≤ z ≤ 10 (amount you want to leave unspent)
y ≥ 1 (amount of dress shirt you need)
This is your system of equation, in which the numbers must fulfill both equations
hope this helps
Https://us-static.z-dn.net/files/d85/2cb87bba0b68f544b98202fa4cd6edf0.png