Let
x----------------> feet of yarn of Becky
y----------------> feet of yarn of James
we know that
4 2/8------> 4 1/4--------> (4*4+1)/4-----> 17/4
1 5/8------> (1*8+5)/8-----> 13/5
x+y=4 2/8-------> x+y=17/4----> equation 1
x=1 5/8--------> x=13/5------> equation 2
substitute 2 in 1
[13/5]+y=17/4------> y=(17/4)-(13/5)----> y=[5*17-4*13]/20
y=(85-52)/20-----> y=33/20----> y=1.65-----> y=1 65/100----> y=1 13/20
the answer is
james have 1 13/20 ft of yarn