Question

The parking lot had 1.5 times more trucks than cars. After 45 more cars came to the parking lot and 12 trucks left, there were 17 more cars than trucks in the parking lot. How many cars were there in the parking lot?
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Answer 1

Let the numbers of trucks and cars be t and c.  Then t = 1.5c.

c+45 - (t-12) = 17.

Simplifying the second equation, we get c + 45 - t - 12 = 17, or c + 33 - t = 17.

Substituting 1.5c for c, we get c + 33 - 1.5c = 17.

Solving this for c, we combine like terms:  -0.5c = 17 - 33, or -0.5c = -16.  

Then c = 32 and t = 1.5(32) = 48.

At the beginning there were 32 cars and 48 trucks in the lot.  Answer:  32 cars, at the beginning.