A sports club charges an initiation fee and a monthly fee. At the end of the 5 months, a member had paid a total of $450. At the end of the 10 months, she had paid a total of $500. a) Write a linear system to model the situation
b) Solve the linear system by substitution to solve the related problem: What are the initiation fee and the monthly fee?

Initiation fee is $400 while monthly fee is $10

Step-by-step explanation:

Let the initial fee be x which is fixed while the monthly fee be y

At the end of 5 months, 450 was paid

This means that;

x + 5y = 450 ••••••••(i)

At the end of 10 months, $500 was paid

Mathematically, this means that;

x + 10y = 500•••••••••••(ii)

now we solve both equations simultaneously to get the value of x and y

our equation ii can be rewritten as;

x + 5y + 5y = 500

we can now insert equation i directly into this

450 + 5y = 500

5y = 500-450

5y = 50

y = 50/5

y = $10

From x + 5y = 450

let’s insert the calculated value of y

x + 5(10) = 450

x + 50 = 450

x = 450-50

x = $400

1) 2/5

2) zero=0/1

3) zero=0/2

4) -4/5

5) undefined=3/0

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)