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.
I don't get it
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
Thank u for this answer it was very helpful.
Thank you so much! This was very helpful.
Well, it seems like the back stockroom at the wheel shop is a real circus! Let's see if we can untangle this puzzle.
Let's assign some variables to make things easier. Let's say "W" is the number of wheels, "S" is the number of seats, "H" is the number of horns, and "HB" is the number of handlebars.
We're given a few key relationships:
1. The number of seats and horns equals the number of wheels: S + H = W
2. The number of seats and handlebars equals the number of horns: S + HB = H
3. Twice the number of wheels is equal to 3 times the number of handlebars: 2W = 3HB
Now, let's try to find the relationship between horns and seats:
From equation 1, we can rearrange it to get: S = W - H
Then we substitute this into equation 2:
(W - H) + HB = H
Simplifying, we get: W + HB = 2H
Now, let's substitute equation 3 into this equation:
W + HB = 2(2W/3)
Simplifying further:
W + HB = 4W/3
Multiplying through by 3:
3W + 3HB = 4W
Subtracting 3HB from both sides:
3W = 4W - 3HB
Subtracting 4W from both sides:
-W = -3HB
And multiplying by -1:
W = 3HB
So we see that the number of wheels is three times the number of handlebars. But what about horns and seats?
From equation 1, we know S + H = W. Since we now know W = 3HB, we can rewrite this as: S + H = 3HB.
Therefore, the relationship between horns and seats is that the number of horns is three times the number of seats.
Voila! We've deciphered the hidden relationship in the wheel shop's stockroom. Remember, it's always good to have a little humor when solving puzzles!
To determine the relationship between horns and seats, let's break down the information provided:
1. In the back stockroom at the wheel shop, the number of seats and horns equaled the number of wheels.
This can be represented as: Seats + Horns = Wheels. ...Equation (1)
2. The number of seats and handlebars equaled the number of horns.
This can be represented as: Seats + Handlebars = Horns. ...Equation (2)
3. Twice the number of wheels is equal to 3 times the number of handlebars.
This can be represented as: 2 * Wheels = 3 * Handlebars. ...Equation (3)
Now, let's solve these equations to determine the relationship between horns and seats:
From Equation (3), we can rearrange it to solve for Wheels:
Wheels = (3/2) * Handlebars.
Now, substitute the value of Wheels from Equation (1) into Equation (3):
Seats + Horns = (3/2) * Handlebars.
Next, substitute the value of Seats + Handlebars (from Equation 2) into Equation (1):
Seats + Horns = (3/2) * (Seats + Handlebars).
Distributing (3/2) to both terms on the right side:
Seats + Horns = (3/2) * Seats + (3/2) * Handlebars.
Now, isolate the Horns term by subtracting (3/2) * Seats from both sides:
Horns = (3/2) * Seats + (3/2) * Handlebars - Seats.
Simplifying the equation:
Horns = (3/2) * Seats - (1/2) * Seats + (3/2) * Handlebars.
Combining like terms:
Horns = (1/2) * Seats + (3/2) * Handlebars.
Therefore, the relationship between horns and seats is:
Horns = (1/2) * Seats + (3/2) * Handlebars.