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 |
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= |
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= |
Graph the lines of the $2$2 equations on the same graph.
State the values of $x$x and $y$y which satisfy both equations.
$x$x = $\editable{}$
$y$y = $\editable{}$
What do the coordinates of the solution mean?
Renting studio $A$A would cost $\$450$$450 to rent for $4$4 hours, which is more than it would cost to rent studio $B$B for the same time.
Renting studio $B$B would cost $\$450$$450 to rent for $4$4 hours, which is more than it would cost to rent studio $A$A for the same time.
Renting either studio $A$A or $B$B for $4$4 hours costs the same amount, $\$450$$450.
The coordinates do not have any real life application.
Consider the following phone plans:
GO SMALL plan: This plan has a $\$20$$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.
A rectangular zone is to be $2$2 cm longer than it is wide, with a total perimeter of $20$20 cm.
The sum of two numbers is $56$56 and their difference is $30$30.