Christine bought 4 sandwiches and 5 bowls of soup, spending $38.50.
Adam spent $47.25 to buy three sandwiches and nine bowls of soup.
What is the cost of each sandwich and each bowl of soup?

place r′ so that qr′ is parallel to the tangent.

now we get that ∠r′py=∠pr′q, where y is on the tangent, on the opposite side of p from x.

also, because of the symmetry, ∠r′py=∠qpx.

finally, note that no matter where we place r, as long as it's on the correct arc, we have ∠prq=∠pr′q.

stringing all these equalities together, we end up with ∠prq=∠qpx.

this picture will show how its going to look like.

hope this by jack monhen

simple 80 pieces in 1 sercing so 80*47=3760+20=3780