SOLUTION: All 1000 parking spaces in my favorite parking lot are filled. Some are occupied by motorcycles and other by cars.Some people count to 10 when they get angry but that wasn�t nearly

Question 1121677: All 1000 parking spaces in my favorite parking lot are filled. Some are occupied by motorcycles and other by cars.Some people count to 10 when they get angry but that wasn�t nearly far enough. I counted wheels �� 3442 to be exact. How many cars and how,any motorcycles have invaded my territory?
(1) which method will be the easiest to understand this problem?
(2) How are they similarly? How are they doffyrf4b

Found 3 solutions by solver91311, Theo, htmentor:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

Let represent the number of 4-wheeled vehicles, then must represent the number of 2-wheeled vehicles, presuming, of course, that none of the 1000 vehicles in the parking lot had a number of wheels that was different than either 2 or 4.

The total number of wheels on the 4-wheeled vehicles must then be and the total number of wheels on the 2-wheeled vehicles must be . These two quantities add up to 3442. So:

Solve for , then calculate

John

My calculator said it, I believe it, that settles it

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
there are 1000 parking spaces and 3442 wheels.
each car 4 wheels.
each motorcycle has 2 wheels.

let x = number of cars and let y = number of motorcycles.

x + y = 1000
4x + 2y = 3442

first equation tells you the number of vehicles, assuming one vehicle in one parking spot.

second equation tells you number of wheels.
since a car has 4 wheels and a motorcycle has 2 wheels, solving these two equations should give you the answer you need.

multiply both sides of the first equation by 4 and leave the second equation as is to get:

4x + 4y = 4000
4x + 2y = 3442

subtract the second equation from the first to gtet:

2y = 558.

solve for y to get y = 558 / 2 = 279.

since x + y = 1000, then x must be equal to 1000 - 279 = 721.

there are 721 cars and 279 motorcycles in the parking lot.

4 wheels per car equals 4 * 721 = 2884 wheels on the cars.

2 wheels per motorcycle equals 2 * 279 = 558 wheels on the motorcycles.

the total number of wheels is 2884 + 558 = 34442.

solution is confirmed to be good.

solution is 721 cars and 279 motorcycles.

Answer by htmentor(1343)   (Show Source): You can put this solution on YOUR website!
Let C = the number of cars
Let M = the number of motorcycles
Since all 1000 spaces are occupied by either cars or motorcycles, we have:
1000 = C + M -> C = 1000 - M
The number of wheels is 3442 = 4C + 2M, since cars have 4 wheels and motorcycles have 2
3442 = 4(1000 - M) + 2M
Solve for M:
3442 - 4000 = -2M
M = 279
Thus C = 1000 - 279 = 721
Number of cars = 721
Number of motorcycles = 279
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