The Hard Cow Math Problem

As promised, here's the problem my cousins and I spend Christmas Eve doing while the little kids opened presents. There are 100 cows and 100 barrels of hay. There are 3 distinct sets of cows: standing, laying, and old. Each standing cow eats five barrels of hay. Each laying cow eats three barrels of hay. And every three old cows eats one barrel of hay. There are no more barrels of hay. How many of each kind of cow are there? Years of higher level education makes this problem very difficult. But I bet a C-average 7th grader could have done it faster than me.