number of seats --- s
number of horns --- h
number of wheels -- w
number of handlebars -- b
"number of seats and horns equaled the number of wheels" ---> s + h = w
"the number of seats and handlebars equaled the number of horns" --> s + b = h
"twice the number of wheels is equal to 3 times number of handlebars" --> 2w = 3b
we want h : s, so play around getting rid of b and w
first and last:
w = s+h, w = 3b/2
so s+h = 3b/2
2s + 2h = 3b
b = h-s
in 2s + 2h = 3b
2s + 2h = 3(h-s)
2s + 2h = 3h - 3s
5s = h
then b = h-s = 5s-s = 4s
h = s+b = s+4s = 5s
so h:s = 5s : s = 5 : 1
horns : seats = 5 : 1
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