Answer to Question #131696 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) decide which one of the following two aspects of the situation will be the input value(the independent variable x) and which one will be the output value( the dependent variable y): the number of months and the amount od money that the brothers pay.

C) set up an equation for both brothers' gym fees

Andile:= y

Beki: y=

D) write both equationd in the form of a function:

Andile: f(x)=

Beki: f(x)=

E) Sketch a graph for both functions on the sane coordinate plane, showing clearly which is Andile's function is and which beki's function is.

F) in which month did the two brothers pay the same amount of money?

H) after 12 months, which brother has paid less towards his gym fees than the other brother has?

Answer 1

A) What do the brothers want? They want to join a gym for some months.

And brothers must determine how much they will pay.

Then number of months will be the input value(the independent variable x) and the amount of money that the brothers pay will be the output value( the dependent variable y)

C) Andile and Beki want to join a gym for one year.

Andile: $y=125x, 0\leq x\leq12$

Beki: $y=250+100x, 0\leq x\leq12$

D) write both equationd in the form of a function:

Andile: $f_1(x)=125x, 0\leq x\leq12$

Beki: $f_2(x)=250+100x, 0\leq x\leq12$

E)

F) $f_1(x)=f_2(x)$

$125x=250+100x$

$125x-100x=250$

$25x=250$

$x=10$

The two brothers paid the same amount of money in October.

H)

Andile: $f_1(12)=125\cdot 12=1500$

Beki: $f_2(x)=250+100\cdot12=1450<1500$

After 12 months, Beki has paid less towards his gym fees than Andile.