A number of commuters were on a bus when it started its journey form the bus station. At the first bus stop, 1/7 of the commuters got off. At the second bus stop, 1/6 of the remaining commuters got off, .... At the sixth bus stop, half the number of commuters got off and the bus was left with only 4 commuters. How many commuters boarded the bus at the bus station?

Question

A number of commuters were on a bus when it started its journey form the bus station. At the first bus stop, 1/7 of the commuters got off. At the second bus stop, 1/6 of the remaining commuters got off, .... At the sixth bus stop, half the number of commuters got off and the bus was left with only 4 commuters. How many commuters boarded the bus at the bus station?

Answer 1

Let x = A of the commuters who boarded the bus at the bus station

x (1 - 1/7) (1 - 1/6) (1 - 1/5) (1 - 1/4) (1 - 1/3) (1 - 1/2) = 4
x (6/7) (5/6) (4/5) (3/4) (2/3) (1/2) = 4
x (1/7) = 4
x = 28

Answer 2

Let's solve this problem step-by-step:

Step 1: Let's assume the number of commuters who boarded the bus at the bus station is "x".

Step 2: At the first bus stop, 1/7 of the commuters got off. Therefore, the number of commuters remaining on the bus is 6/7 times x.

Step 3: At the second bus stop, 1/6 of the remaining commuters got off. Therefore, the number of commuters remaining on the bus now is 5/6 times (6/7 times x) = 5/7 times x.

Step 4: Repeating the process, at the third bus stop, the number of commuters remaining on the bus is 4/5 times (5/7 times x) = 4/7 times x.

Step 5: At the fourth bus stop, the number of commuters remaining on the bus is 3/4 times (4/7 times x) = 3/7 times x.

Step 6: At the fifth bus stop, the number of commuters remaining on the bus is 2/3 times (3/7 times x) = 2/7 times x.

Step 7: Finally, at the sixth bus stop, half the number of commuters got off. Therefore, the number of commuters remaining on the bus now is 1/2 times (2/7 times x) = 1/7 times x.

Step 8: According to the given information, the bus was left with only 4 commuters. So, we can write the equation: 1/7 times x = 4.

Step 9: To solve for x, we can multiply both sides of the equation by 7: x = 4 * 7 = 28.

Therefore, the number of commuters who boarded the bus at the bus station is 28.

Answer 3

To solve this problem, let's work through it step by step.

Let's assume the number of commuters who boarded the bus at the bus station is 'x'.

At the first bus stop, 1/7 of the commuters got off. This means that 6/7 of the commuters remain on the bus.
So, after the first bus stop, the number of commuters remaining on the bus is (6/7)x.

At the second bus stop, 1/6 of the remaining commuters got off. This means that 5/6 of the commuters remain on the bus.
So, after the second bus stop, the number of commuters remaining on the bus is (5/6) * (6/7)x = (5/7)x.

We can repeat this process for the remaining bus stops.

At the third bus stop, the number of remaining commuters is (4/5) * (5/7)x = (4/7)x.
At the fourth bus stop, the number of remaining commuters is (3/4) * (4/7)x = (3/7)x.
At the fifth bus stop, the number of remaining commuters is (2/3) * (3/7)x = (2/7)x.

At the sixth bus stop, half the number of commuters remaining on the bus got off, leaving only 4 commuters. So, (1/2) * (2/7)x = 4.

Simplifying, we have (1/7)x = 4.
Multiplying both sides by 7, we get x = 4 * 7.
Therefore, the number of commuters who boarded the bus at the bus station is 28.

So, 28 commuters boarded the bus at the bus station.

Answer 4

Well, it looks like this bus ride was full of ups and downs, just like a roller coaster! Let's break it down step by step.

At the first bus stop, 1/7 of the commuters got off. So, if we call the total number of commuters at the beginning "x," then after the first stop, the number of remaining commuters will be (6/7)x.

At the second bus stop, 1/6 of the remaining commuters got off. So, after this stop, the number of remaining commuters will be (5/6)(6/7)x.

Now, let's keep going. At each subsequent stop, we'll multiply the fraction of remaining commuters by the fraction of commuters that got off. We do this until the sixth bus stop.

So, after the sixth stop, the number of remaining commuters is (1/2)(4).

Now, we can set up the equation:

(1/2)(4) = (5/6)(6/7)(4) (canceling out common factors)

Simplifying, we get:

2 = (5/7)(4)

Now, we only need to solve for the total number of commuters, x. We can do this by multiplying both sides by the reciprocal of (5/7):

2 * (7/5) = x

And finally, we find:

x = 14

So, it seems that 14 commuters boarded the bus at the bus station at the beginning of the journey! I hope they had their tickets ready!