The only types of vehicles sold at a certain dealership last month were sedans, trucks, and vans. If the ratio of the number of sedans to the number of trucks to the number of vans sold at the dealership last month was 4:5:7, respectively, what was the total number of vehicles sold at the dealership last month?1) The number of vans sold at the dealership last month was between 10 and 20.
2) The number of sedans sold at the dealership last month was less than 10.

We know that the ratio of the number of sedans to the number of trucks to the number of vans sold at the dealership last month was 4:5:7, respectively. We have :

[tex]4:5:7 \implies 4x+5x+7x=16x[/tex]

Therefore, 16x is he total number of vehicles sold at the dealership last month.

We know that:

1) The number of vans sold at the dealership last month was between 10 and 20.

2) The number of sedans sold at the dealership last month was less than 10

We get:

[tex]10\leq 7x \leq 20\\\implies x=2\\\\\\4x\leq 10\\x=1 \, \vee \, x=2[/tex]

We know that x is a positive integer. In order to satisfy both conditions, this is possible only if x = 2.

We get [tex]16x=16\cdot 2=32[/tex]

Therefore, 32 is he total number of vehicles sold at the dealership last month.