Four students plan to rent a minivan for a weekend trip and equally share the rental cost of the van. By adding two more people, each persona can save $10 on his or her shre of the cost. How much is the total rental cost of the van?

The total rental cost is $120.

Let x be the amount each person pays and y be the total cost.  Our first equation would be 
4x = y.

The second equation would be
6(x-10) = y.

Since these are set equal to the same variable, we can use substitution:
4x = 6(x-10)

Using the distributive property, we have
4x = 6*x - 6*10
4x = 6x-60

Subtract 4x from both sides:
0 = 2x-60

Add 60 to both sides;
60 = 2x

Divide both sides by 2:
30 = x

This means each person pays $30 (in the first equation).  4(30) = 120 for y.

With 4 people, each person pays $30; with 6 people, each person pays 30-10=20.