A company uses two vans to transport workers between 7:00 and 9:00 am. One van has 5 more seats than the other. The smaller van makes two trips every morning while the larger one makes only one trip. Two vans can transport 71 people maximum. Let X be the seats in the small van l and y the seats in the larger van. How many seats does the larger van have???

Accepted Solution

Hello!The answer is: 27 seatsWhy?Let's make the equations with the given information:[tex]x=SmallVanSeats\\y=LargeVanSeats[/tex]Then, if the larger van has five (5) more seats than the smaller van:[tex]y-x=5[/tex]So, if the smaller van makes two trips and the larger just makes one, transporting a maximum of 71 people:[tex]y+2x=71[/tex]By substituting equation 1 into equation 2, we have:[tex](5+x)+2x=71\\3x=71-5\\3x=66\\x=\frac{66}{3}=22[/tex]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:[tex]y-22=5\\y=22+5=27[/tex]So, the larger van has 27 seats.Have a nice day!