there are 21 seats and 54 wheels in a bicycle and go-carts. how many and bicycles and go carts are there

Question

i solved the question there are 21 bicycles with 42 wheels and 3 go carts with 12 wheels is there another way to solve

Answer 1

That's using brute force.  There is also a logical/algorithmic approach.  Reading the details we get:

 

  Re seats: b + g = 21

     (one seat per vehicle, hence bikes plus go-carts is 21 total)

  Re wheels: 2b + 4g = 54

     (2 wheels per bike + 4 wheels per gocart is 54 wheels total)

 

Now "all" we have to do is define one in terms of the other and substitute.  So using the first formula and solving for one of the symbols (I take b, but you could also take g (you could also do this with the second formula but solving for b or g there would end up with a messy result especially when you have to substitute it into the other formula) we get:

 

  b = 21 - g

 

Now, substitute this wherever you see b in the second formula:

 

  2(21 - g) + 4g = 54

 

Solving that would yield:

 

  42 - 2g + 4g = 54

  42 + 2g = 54

  2g = 12

  g = 6

 

If g is 6, then using either formula, but picking the first since it's straightforward, then, b = 15

 

Feeding it back into the English (or either formula) that would yield 21 seats (15 + 6) and 54 wheels (15*2 + 6*4).

Answer 2

Sorry Malikka, that would make 24 seats in all. Go from there, and reduce your bicycles to the next odd number down. For example, 19 bicycles would make 38 wheels, leaving 12 wheels which is 3 go carts. This makes 19+3=22. You're getting close. Keep on till your bicycles and go carts equal 21.