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AustraliaVIC
VCE 11 Methods 2023

1.09 Simultaneous equations

Worksheet
Applications
1

Kerry currently pays \$50 a month for her internet service. She is planning to switch to a fibre optic cable service.

a

Write an equation for the total cost T of Kerry's current internet service over a period of n months.

b

For the fibre optic cable service, Kerry pays a one-off amount of \$1200 for the installation costs and then a monthly fee of \$25. Write an equation of the total cost T of Kerry's new internet service over n months.

c

Complete the table for the total cost of the current internet service, given by T = 50 n:

n 1 6 12 18 24
T (\text{ dollars})
d

Complete the table of values for the total cost of the fibre optic cable service, given by T = 25 n + 1200

n 1 6 12 18 24
T (\text{ dollars})
e

Graph the lines for the total cost of Kerry's current internet service and the total cost of her new internet service on a number plane.

f

Using your graph to determine how many months it will take for Kerry to break even on her new internet service.

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Outcomes

U1.AoS2.8

solution of a set of simultaneous linear equations (geometric interpretation only required for two variables) and equations of the form f(x) = g(x) numerically, graphically and algebraically.

U1.AoS2.19

set up and solve systems of simultaneous linear equations involving up to four unknowns, including by hand for a system of two equations in two unknowns

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