Answer to Question #132215 in Algebra for Ayanda Sikhosana

Question

Two brothers, Andile and Beki, want to join a gym for one year. 

Andile decides to join Gym Aerolux and Beki decides to join 

Gym Bodyworx. The monthly fee for Aerolux is R125 with no 

registration fee and the monthly fee for Bodyworx is R100 with 

R250 registration fee.

a) In which one of the two functions do we see a direct proportion between the number 

of months and the fees paid?

Answer 1

Direct proportion is the relation between quantities whose ratio is

constant.

Here, the monthly fee for Aerolux is R125 with no registration fee

so, total fee Andlie needs to pay in one year is $R125 * 12 = R1500$

$\therefore$ Ratio of no. of months to the amount of fees paid is $\dfrac{1500}{12} = 125,$ which is a

constant. Hence, here we see a direct proportion.

Again, the monthly fee for Bodyworx is R100 with

 R250 registration fee (which is paid one time).

So, total fee Beki needs to pay in one year is $R100 * 12 + R250 =R1200 +R250=R1450$

$\therefore$ Ratio of no. of months to the amount of fees paid is $\dfrac{1450}{12} = 120.833$ .which is not a

constant. Hence, we do not see a direct proportion here.