What are the values of u and v

More algebra pretending to be geometry.  What a waste.

The corresponding sides have to be congruent so this is a linear system with two equations in two unknowns,

8v - 4u + 28 = u + v

v + 2u + 26 = 17v - 3u

7v - 5u + 28 = 0

-16v + 5u + 26 = 0

Adding equations,

-9v + 54 = 0

-9v = -54

v = 6

5u = 7v + 28 =  42 + 28 = 70

u = 14

u=14, v=6

Check:

8v - 4u + 28 = 8(6) - 4(14) + 28 = 20

u + v = 14 + 6 = 20, good

v + 2u + 26 = 6 + 2(14) + 26 =  32+28 = 60

17v - 3u = 17(6) - 3(14) = 6(17- 7) = 60, good

10 glasses of juice could be made with 5 carrots, 1,500 orange juice, 2,000 papaya juice.