SOLUTION: A traffic check counted 390 cars passing a certain spot on one day and 430 cars at the same spot on the second day. The first day there were 3 times as many cars going east and ha
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Question 30876: A traffic check counted 390 cars passing a certain spot on one day and 430 cars at the same spot on the second day. The first day there were 3 times as many cars going east and half as many cars going west on the second day. What was the total number of east bound cars and the total number of west bound cars for two days? Answer by mbarugel(146) (Show Source):
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Let's call X to the number of cars going EAST on the 1st day and Y to the number of cars going WEST on the 1st day.
We can use the information given in the problem to form a simple system of equations and find X and Y. We know:
"A traffic check counted 390 cars passing a certain spot on one day"
This implies that
[recall that X and Y are cars in the FIRST day]
We also know that:
"The first day there were 3 times as many cars going east and half as many cars going west on the second day"
This implies that the second day there were X/3 cars going east (because the 1st day had 3 times as many cars going east on the 2nd day) and 2Y cars going west (because the on the first day there were half as many cars going west on the 2nd day).
So the total number of cars in the second day was X/3 + 2Y. We also know that this number is 430. So we get the system:
You can solve this system with your preferred method. Here's the solution using substitution:
Solve: We'll use substitution. After moving 1*y to the right, we get: , or . Substitute that
into another equation: and simplify: So, we know that y=180. Since , x=210.
Answer: .
So there were 210 cars going east and 180 cars going west in the 1st day, for a total of 390 cars. The second day, there were X/3 = 70 cars going east and 2Y = 360 cars going west, for a total of 430 cars.
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