The U-Drive Rent-A-Truck company plans to spend $\$ 14$ million on 280 new vehicles. Each commercial van will cost $\$ 55,000$, each small truck $\$ 20,000$, and each large truck $\$ 70,000$. Past experience shows that they need twice as many vans as small trucks. How many of each type of vehicle can they buy? They can buy $\square$ vans, $\square$ small trucks, and $\square$ large trucks.

Step 1 ：Let's denote the number of vans as v, the number of small trucks as s, and the number of large trucks as l. We know that the total cost of all vehicles is \$14,000,000. This gives us the equation: \(55000v + 20000s + 70000l = 14000000\)

Step 2 ：We also know that the number of vans is twice the number of small trucks, which gives us the equation: \(v = 2s\)

Step 3 ：We can substitute the second equation into the first to get an equation with two variables. Then we can solve this system of equations to find the number of each type of vehicle. The substituted equation is: \(70000l + 130000s = 14000000\)

Step 4 ：We have found the solution in terms of v, s, and l. However, we need to find the actual number of each type of vehicle. We know that v, s, and l must be integers because we cannot buy a fraction of a vehicle. Therefore, we can iterate over possible values of v and s until we find a solution where l is also an integer.

Step 5 ：Final Answer: They can buy \(\boxed{210}\) vans, \(\boxed{35}\) small trucks, and \(\boxed{35}\) large trucks.