Question 1080325: A traffic check counted 390 cars passing a certain spot on one day and 430 cars at the same spot of the second day. On the first day, there are three times as many cars going east and half as many going west as on the second day. What was the total number of eastbound cars and the total number of west bound cars for the two days? How many are:
(a) East? (b) West?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = number of cars going eastbound
let y = number of cars going westbound.
on day 1 you have 3 times as many cars going eastbound as on day 2.
on day 1 you have 1/2 as many cars going westbound as on day 2.
draw a table similar to one shown below:
east west total
day 1 3x y 390
day 2 x 2y 430
total 4x 3y 820
since 3x is 3 times x, your first requirements is satisfied because 3 times as many cars are going east on day 1 as on day 2.
since y is 1/2 of 2y, your second requirement is satisfied because 1/2 as many cars are going west on day 1 as on day 2.
you have 2 equations that need to be solved simultaneously.
they are:
3x + y = 390
x + 2y = 430
multiply both sides of the first equation by 2 and leave the second equation as is to get:
6x + 2y = 780
x + 2y = 430
subtract the second equation from the first to get:
5x = 350
solve for x to get x = 530 / 5 = 70
in the first original equation, solve for y as follows:
start with 3x + y = 390
replace x with 70 to get 3*70 + y = 390
simplify to get 210 + y = 390
subtract 210 from both sides to get y = 390 - 210
simplify to get y = 180
you have:
x = 70
y = 180
substitute in both original equation to get:
3x + y = 390 becomes 3*70 + 180 = 390 which becomes 210 + 180 = 390 which becomes 390 = 390 which is true.
x + 2y = 430 becomes 70 + 2*180 = 430 which becomes 70 + 360 = 430 which becomes 430 = 430 which is true.
the solutions look good.
the question was how many cars were eastbound total and how many cars were westbound total.
3x + x = 4x = 4*70 = 280
y + 2y = 180 + 360 = 540
total cars both ways for both days = 820
total of 280 were eastbound
total of 540 were westbound
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