System of equations word problem?

A Honda dealership sells both motorcycles and cars. THere area total of 200 vehicles on the dealership's lot. THe detailer cleaned all the wheels of all the vehicles, which totaled 698 wheels. How many motorcycles are there on the on the lot?

There are 200 vehicles on the lot. If those 200 vehicles were all motorcycles, there would be 400 wheels. For every one of those vehicles that's a car instead of a motorcycle there will be 2 extra wheels. So 698-400 = 298 extra wheels. That means 298/2 cars or 149 cars. 200-149 is 51 so there are 51 motorcycles.

So now to check, we have 149 cars * 4 wheels each = 596 wheels. And 51 motorcycles * 2 wheels is 102 wheels. 596 + 102 = 698. So I'm right! Yaaaaaay!

Mr Smartypants answer using logic is correct - but that is no help for someone learning systems of equations!

There are 51 motorcycles

Let the number of motorcycles = M and the number of cars = C
We know there are 200 vehicles, therefore M + C = 200
From this - by rearranging we determine that M = 200 - C. (Call this Equation 1)

We also know that there are 698 wheels
Therefore as a motorcycle has 2 wheels and a car has 4 wheels
2M + 4C = 698 (call this Equation 2)

BUT we know from Equation 1 that M = 200 - C, therefore substitute this amount (200 - C) for "M" in Equation 2 which then becomes
2(200 - C) + 4C = 698
Expand the bracket
400 - 2C + 4C = 698
400 + 2C = 698
2C = 298
C = 149
Therefore there are 149 cars
As there are 200 vehicles then the number of motorcycles = 200 - 149 = 51

Check
51 motorcycles * 2 wheels = 102 wheels
149 cars * 4 wheels = 596 wheels
Total 200 vehicles and 698 wheels = correct

ELIMINATION METHOD

M + C = 200 (Eq 1)
2M + 4C = 698 (Eq 2)

Multiply Equation 1 by 2 and leave Equation 2 as it is

2M + 2C = 400
2M + 4C = 698
Subtract top from bottom

(2 - 2)M + (4 - 2)C = 698 - 400
2C = 298
C = 298 / 2
C = 149

As there are 200 vehicles M = 200 - 149 = 51
Do the same check as above