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?
Accepted Solution
A:
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.