Question

a company uses two vans to transport workers from a free parking lot to the workplace between 7:00 and 9:00 am . one van has 6 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 57 people , maximum. let X be the seats in the small van and y the seats in the large van . how many seats does the larger van have?

Answer 1

The larger van has 15 seats.

Step-by-step explanation:

Let's denote the number of seats in the smaller van as X and the number of seats in the larger van as Y.

We know that the smaller van makes two trips every morning, so it can transport a maximum of 2 * X people. On the other hand, the larger van makes only one trip, so it can transport a maximum of Y people.

According to the problem, the two vans can transport 57 people maximum. Using this information, we can set up the following equation:

2X + Y = 57

It's also mentioned that the smaller van has 6 more seats than the larger van. So we can express X in terms of Y as:

X = Y + 6

To find the number of seats in the larger van, we need to solve this system of equations. Substituting the value of X in the first equation, we get:

2(Y + 6) + Y = 57

Simplifying the equation:

2Y + 12 + Y = 57

3Y + 12 = 57

3Y = 45

Y = 15

Therefore, the larger van has 15 seats.

Answer 2

y - x = 6
y + 2x = 57

2y - 2x =12
y + 2x = 57

∴3y = 69
y = 23


23 - x = 6
-x = -17
x =17

large van = 23
small van = 17