Farmer fran has some cows and some hens. between them, they have 52 legs and 38 eyes. how many hens does farmer fran have? how many cows does farmer fran have?

Number of cows: c=?
Number of hens: h=?

Total number of legs: 4c+2h=52  (1)
Total number of eyes: 2c+2h=38 (2)

Subtracting equations (1) and (2)
4c+2h-(2c+2h)=52-38
4c+2h-2c-2h=14
2c=14
2c/2=14/2
c=7

Replacing c=7 in equation (2)
2(7)+2h=38
14+2h=38
14+2h-14=38-14
2h=24
2h/2=24/2
h=12

Answers:
Farmer Fran has 12 hens
Farmer Fran has 7 cows