A 26 seater bus and 14 matatu were to transport 494 Pupils.if the matatu made an extra trip than the bus,how many pupils did the matatu transport?
number of trips made by bus ---- x
number of trips made by matatu ---- x+1
26x + 14(x+1) = 494
solve for x, then evaluate 14(x+1)
182 pupils
Correct!
The solution for x is:
26x + 14(x+1) = 494
Expanding the brackets and simplifying:
40x + 14 = 494
40x = 480
x = 12
So the bus made 12 trips, and the matatu made 13 trips.
To find out how many pupils the matatu transported:
14(x+1) = 14(12+1) = 14(13) = 182
Therefore, the matatu transported 182 pupils.
182
Yes, that's correct! The matatu transported 182 pupils.
Well, if we subtract the number of pupils transported by the bus from the total number of pupils, we can find out how many pupils the matatu transported.
Let's do the math:
494 - 26 = 468
So, the matatu transported 468 pupils. But remember, the matatu made an extra trip, so we need to divide this number by 2 to get the number of pupils per trip.
468 ÷ 2 = 234
Therefore, the matatu transported 234 pupils per trip.
To solve this problem, we can set up an equation. Let's say the number of pupils transported by the bus is x, and the number of pupils transported by each matatu is y.
Given that there are 26 seats in the bus, the bus can transport a maximum of 26 pupils. And since there are 14 matatus, collectively, the matatus can transport a maximum of 14 * y pupils.
According to the problem, the matatu made an extra trip than the bus. This means that the number of trips made by the matatu is one more than the number of trips made by the bus. Since both the bus and matatu have to transport all the pupils, the number of trips made by the bus would be equal to the number of pupils transported by the bus divided by the number of seats in the bus (x / 26). Similarly, the number of trips made by each matatu would be equal to the number of pupils transported by each matatu divided by the number of seats in the matatu (y / seats_in_the_matatu).
We know that the number of trips made by the matatu is one more than the number of trips made by the bus. So, the equation becomes:
x / 26 = (14 * y) / seats_in_the_matatu + 1
To find the value of y (the number of pupils transported by each matatu), we need to relate the number of trips made by the matatu to the number of trips made by the bus. We can do this by equating the two expressions for the number of trips:
x / 26 = (14 * y) / seats_in_the_matatu + 1
Now, we can solve the equation to find the value of y (the number of pupils transported by each matatu).
But before we can solve for y, we need to know the number of seats in each matatu. Please provide the number of seats in each matatu.