Answer to Question #212842 in Algebra for Zee

Question

The parking garage at a train station offers two monthly payment plans for customers. Both plans consist of a fixed monthly cost plus an additional cost per day. Plan A charges a fixed monthly fee of R55

 plus R21

 per day. The total cost for parking under plan B for a certain number of days is given in the table below:

Number of

days parked     Cost     

(R)3

106

10

260

18

436

20

480

 

If C

 represents the total monthly parking cost of a client and n

 represents the number of times he parks his vehicle, which ONE of the following systems of equations best represents this situation?

Answer 1

Plan A

$$C_A=55+21n$$

Plan B

$$C_B(3)=b+m(3)=106$$

$$C_B(10)=b+m(10)=260$$

$$10m-3m=260-106$$

$$7m=154$$

$$m=22$$

$$b+22(3)=106$$

$$b=40$$

$$C_B=40+22n$$

$$55+21n\geq40+22n$$

$$n\leq15$$

If $n\leq15$ days, Plan B is better.

If $n\geq15$ days, Plan A is better.