souma730 wrote:Cars emerging from a motorway arrive at a junction that splits the road into two separate lanes. The number of cars per hour that continue in either lane is constant. If 700 cars per hour were diverted from the left lane to the right lane, the number of cars entering the right lane per hour would be twice as big as the number of cars entering the left lane per hour. Alternatively, if 700 cars per hour were diverted from the right lane to the left lane, the number of cars entering the left lane per hour would be four times as great as the number of cars entering the right lane per hour. How many cars enter the left lane per hour?
A. 1300
B. 1500
C. 1700
D. 1900
E. 2100
Let L = # of cars that enter left lane per hour
Let R = # of cars that enter right lane per hour
If 700 cars per hour were diverted from the left lane to the right lane...
So, L - 700 = cars per hour in the left lane
And R + 700 = cars per hour in the right lane
...the number of cars entering the right lane per hour would be twice as big as the number of cars entering the left lane per hour
So,
2(L - 700)= R + 700
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If 700 cars per hour were diverted from the right lane to the left lane...
So, L + 700 = cars per hour in the left lane
And R - 700 = cars per hour in the right lane
... the number of cars entering the left lane per hour would be four times as great as the number of cars entering the right lane per hour
So,
L + 700= 4(R - 700)
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We now have the following system:
2(L - 700)= R + 700
L + 700= 4(R - 700)
Expand and simplify to get:
2L - 2100 = R
L + 3500 = 4R
Multiply blue equation by 4 to get:
8L - 8400 = 4R
L + 3500 = 4R
Now that both equations are set equal to 4R, we can write the following:
8L - 8400 =
L + 3500
Rearrange: 7L = 11,900
Solve: L =
1700
Answer:
C
Cheers,
Brent
