SOLUTION: A taxi is rented by a group of x people for $40 and the cost is shared equally. If there is one less person in the group then the difference between the two payments (that is, the

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A taxi is rented by a group of x people for $40 and the cost is shared equally. If there is one less person in the group then the difference between the two payments (that is, the       Log On


   

Question 1153472: A taxi is rented by a group of x people for $40 and the cost is shared equally. If there is one less person in the group then the difference between the two payments (that is, the payments by an individual in each case) is less than $2. What are the possible values for x?
Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


A formal algebraic solution will be somewhat complicated....

So solve the problem with trial and error, a little mental arithmetic, and logical reasoning.

Obviously the number of people has to be a whole number; and it needs to be a number that is reasonable, assuming the "taxi" is not a bus.

5 people paying $40 means $8 each; 4 people paying $40 means $10 each. That difference is EXACTLY $2; logical reasoning then tells us that if the difference is LESS THAN $2, the original number of people has to be MORE THAN 5.

ANSWER: The number of people has to be greater than 5.

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
                      PRICE            PEOPLE       COST

Is Rented              40/x              x           40

If One less person     40/(x-1)         x-1          40

Price Difference         2

0%3C40%2F%28x-1%29-40%2Fx%3C2assumingnaturalnumber

-

20%2F%28x-1%29-20%2Fx%3C1

20%2F%28x-1%29-20%2Fx-1%3C0

20x-20%28x-1%29-x%28x-1%29%3C0

20x-20x%2B20-x%5E2%2Bx%3C0

20-x%5E2%2Bx%3C0

-x%5E2%2Bx%2B20%3C0

x%5E2-x-20%3E0
%28x%2B4%29%28x-5%29%3E0

x=6 is one example that will work.
graph%28400%2C400%2C-2%2C8%2C-2%2C8%2C%28x%2B4%29%28x-5%29%29