Writing an Algebraic Expression

by Cyndy
(United States)

Question
If n is equal to the number of rides and 1 ride is 2.00 and 2 rides is 2.50, write an expression using n to show the cost.

Answer
Base on the information given, the expression that we are going to write is only valid for 1 and 2 rides.

Let's list down the information:

Number of Ride (n)Cost
12.00
22.50


Let the cost of the rides be C.

Hence, when n = 1, we have:
C = 2.00    ----- (1)

When n = 2, the cost increase by 0.50. Hence:
C = 2.00 + 0.50    ----- (2)

To write an expression that caters for (1) and (2), note that in (2), we can multiply the term, 0.50, with (n-1) as shown:
C= 2.00 + 0.50(n-1)    ----- (3)

Why? This is because the (n-1) will help to remove the 0.50 term when n =1. This is shown below:
C = 2.00 + 0.50(1-1)
 = 2.00 + 0.50(0) 
= 2.00                  

And, when n = 2, the (n-1) will help to retain the 0.50. This is shown below:
C = 2.00 + 0.50(2-1)
 = 2.00 + 0.50(1)
= 2.00 + 0.50    
= 2.50                 

Hence, the expression that we are looking for is:
C = 2.00 + 0.50(n-1)        For n =1 and n =2






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