14 pointslet x be the seats in the small van and y the seats in the large van. how many seats does the large van have? a company uses two vans to transport worker from a free parking lot to the workplace between 7: 00 and 9: 00a. m. one van has 9 more seats than the other. the smaller van makes two trips every morning while the larger one makes only one trip. the two vans can transport 69 people, maximum. how many seats does the larger van have?
y = x + 5
2x + (x + 5) = 71
3x + 5 = 71
3x = 71 - 5
3x = 66
x = 66/3
x = 22 small van
y = x + 5
y = 22 + 5
y = 27 <=== larger van
14 more seats than the other
so L = larger S=smaller
both transport 65 people
31 gives L 14 More Seats Than S
Let the number of seats in the smaller van =x
One van has 14 more seats than the other.
Therefore, the number of seats in the larger van y= x+14The smaller van makes two trips every morning while the larger one makes only one trip. The two vans can transport 65 people, maximum.
Two trips of the smaller Van+ One Trip of the Larger Van=65
Therefore, the number of seats in the larger van, y=17+14
Let x be the smaller van, and y be the larger one.
We know that y = x + 14
We also know that 2x + y = 65
If we replace y by its value in the second equation we have:
2x + (x + 14) = 65, then we solve
2x + x + 14 = 65
3x + 14 = 65
3x = 51
x = 17
We now know the smaller van has 17 seats.
To find how many seats are in the big one, we take the first equation:
y = x + 14
y = 17 + 14
y = 31
14 - 65 = 51
x=20 seats, y=29 seats
2x+y=69 solve by substitution
x=60/3=20 (small van)
y=29 (large van)
let van 1 seats = x
let van 2 seats = y = x + 6
Total # trips larger = 1 trip
total # trips small = 2 trips
max # people = 57 each
2x + y = 57
2x + (x + 6) = 57
3x = 51
x = 51/3 = 17 people
y = x + 6 = 17 + 6 = 23 people
check: 2x + y = 57 2(17) + 23 = 34 + 23 = 57
Thus, the small van can carry 17 passengers the large van can carry 23 passengers
The answer is: 27 seatsWhy?
Let's make the equations with the given information:
Then, if the larger van has five (5) more seats than the smaller van:
So, if the smaller van makes two trips and the larger just makes one, transporting a maximum of 71 people:
By substituting equation 1 into equation 2, we have:
So, the smaller van has 22 seats, to find how many seats has the larger van we just need to substitute the number of seats of the smaller van into the first equation:
So, the larger van has 27 seats.
Have a nice day!