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6.045 Applications of simultaneous equations

Interactive practice questions

A band plans to record a demo at a local studio. The cost of renting studio $A$A is $\$250$$250 plus $\$50$$50 per hour. The cost of renting studio $B$B is $\$50$$50 plus $\$100$$100 per hour.

The cost, $y$y, in dollars of renting the studios for $x$x hours can be modelled by the linear system:

Studio $A$A $y$y $=$= $50x+250$50x+250
Studio $B$B $y$y $=$= $100x+50$100x+50
a

What are the $x$x- and $y$y-values of the intercepts of the line $y=50x+250$y=50x+250?

$x$x-intercept $x=\editable{}$x=
$y$y-intercept $y=\editable{}$y=
b

What are the $x$x- and $y$y-values of the intercepts of the line $y=100x+50$y=100x+50?

$x$x-intercept $x=\editable{}$x=
$y$y-intercept $y=\editable{}$y=
c

Graph the lines of the $2$2 equations on the same graph.

Loading Graph...
d

State the values of $x$x and $y$y which satisfy both equations.

$x$x = $\editable{}$

$y$y = $\editable{}$

e

What do the coordinates of the solution mean?

Renting studio $A$A would cost $\$450$$450 to rent for $4$4 hours, which is more than it would cost to rent studio $B$B for the same time.

A

Renting studio $B$B would cost $\$450$$450 to rent for $4$4 hours, which is more than it would cost to rent studio $A$A for the same time.

B

Renting either studio $A$A or $B$B for $4$4 hours costs the same amount, $\$450$$450.

C

The coordinates do not have any real life application.

D
Easy
5min

Consider the following phone plans:

GO SMALL plan: This plan has a $\$20$$20 monthly base charge and charges $90$90 cents per minute for all calls.

GO MEDIUM plan: This plan has a $\$26$$26 monthly base charge and then charges $70$70 cents per minute for all calls.

Easy
7min

A rectangular zone is to be $2$2 cm longer than it is wide, with a total perimeter of $20$20 cm.

Medium
5min

The sum of two numbers is $56$56 and their difference is $30$30.

Medium
2min
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Outcomes

MA11-1

uses algebraic and graphical techniques to solve, and where appropriate, compare alternative solutions to problems

MA11-2

uses the concepts of functions and relations to model, analyse and solve practical problems

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