three fifths of my cattle are Jerseys; the rest are Herefords.
Three quarters of my Jerseys are female, as are three eights of my Herefords
(a) What fracrtion of my cattle are females?
(b) what fraction of my male cattle are Herefords?
OK here goes -
three fifths are Jerseys and of these three quarters are female so female jersey cows are:
three fifths x three quarters = 3/5 x 3/4 = 9/20
for the Herefords
two fifths must be Herefords and we're told three eights of these are female:
2/5 x 3/8 = 6/40 = 3/20
so total females are 9/20 + 3/20 = 12/20 = 3/5
(b) if 3/5 of the herd are female 2/5 are male - so what fraction of these are Herefords?
of these male animals (3/5 x 1/4 = 3/20) are Jerseys and (2/5 x 5/8 = 5/20) are Herefords so 5/8 of the males are Herefords I think