# Math

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in the back stockroom at the wheel shop, the number of seats and horns equaled the number of wheels. the number of seats and handlebars equaled the number of horns. twice the number of wheels is equal to 3 times number of handlebars. Determine the relationship of horns to seat.

• Math - ,

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

from 2nd:
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
from above:
h = s+b = s+4s = 5s

so h:s = 5s : s = 5 : 1

horns : seats = 5 : 1

• Math - ,

I don't get it

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