The first car of the D-line train carried 1.5 times the number of passengers that the second car carried. Three passengers get out of the first car at Newton Center and two passengers get into the second car at the same station. After this stop both cars had an equal number of passengers. How many passengers were in each car before the Newton Center stop?
start writing what they tell you. If the 1st car had 3x and the 2nd car had 2x (because the ratio was 3:2) then
3x-3 = 2x+2
x = 5
So the two cars had 15 and 10 passengers, respectively.
Check: 15-3 = 10+2
Let's assume the number of passengers in the second car before the Newton Center stop is x.
According to the problem, the first car carried 1.5 times the number of passengers in the second car, so the number of passengers in the first car before the Newton Center stop is 1.5x.
After three passengers get out of the first car at Newton Center, the number of passengers in the first car becomes 1.5x - 3.
Similarly, after two passengers get into the second car at Newton Center, the number of passengers in the second car becomes x + 2.
After these changes, both cars have an equal number of passengers, so we can set up the equation:
1.5x - 3 = x + 2
Simplifying this equation:
1.5x - x = 2 + 3
0.5x = 5
Dividing both sides by 0.5:
x = 10
Therefore, there were 10 passengers in the second car before the Newton Center stop.
Since the first car carried 1.5 times the number of passengers in the second car, there were 1.5 * 10 = 15 passengers in the first car before the Newton Center stop.
So, there were 15 passengers in the first car and 10 passengers in the second car before the Newton Center stop.
To solve this problem, we can set up an equation based on the information given.
Let's assume that the second car had x passengers initially. According to the question, the first car carried 1.5 times the number of passengers as the second car, so it had 1.5x passengers initially.
After three passengers got out of the first car at Newton Center, the number of passengers in that car became 1.5x - 3. Similarly, after two passengers got into the second car at Newton Center, the number of passengers in that car became x + 2.
According to the question, after this stop, both cars had an equal number of passengers. Therefore, we can set up the following equation:
1.5x - 3 = x + 2
Now, let's solve this equation to find the value of x.
1.5x - x = 2 + 3
0.5x = 5
x = 5/0.5
x = 10
So, the second car initially had 10 passengers.
To find the number of passengers in the first car before the Newton Center stop, we can substitute the value of x back into one of the expressions. Let's use the expression for the first car's initial passengers:
1.5x = 1.5 * 10 = 15
Therefore, the first car initially had 15 passengers.
To summarize, before the Newton Center stop, the first car had 15 passengers and the second car had 10 passengers.