Question 7
Jack and Jill each sell the same number of eggs daily. Jack sells 2 eggs for 5 baht and earns $a$ baht; Jill sells 3 for 7 baht and earns $b$. One day Jill sells both equal stocks together at 5 eggs for 12 baht, earning $c$. If $a:b:c=x:y:z$ for positive integers $x,y,z$, find the minimum $x+y+z$.