Interactive practice questions
A family owns two businesses that made a combined profit of $\$6$$6 million in the previous financial year, with business B making $2$2 times as much profit as business A.
Let $x$x and $y$y be the profits ( in millions) of business A and business B respectively.
Use the fact that the two businesses made a combined profit of $\$6$$6 million to set up an equation involving $x$x and $y$y.
Use the fact that business B made $2$2 times as much as business A to set up another equation relating $x$x and $y$y.
Which of the following sets of graphs correctly depicts the two equations?
Use the graph to find business A's profit.
Use the graph to find business B's profit.
Two twin soccer players are having a contest over who will score the most goals in the season. The twins have scored a combined total of $34$34 goals so far over the season and twin A has scored $6$6 more goals than twin B.
Let $x$x and $y$y be the number of goals scored by twin A and twin B respectively.
A family returns home from a trip in two separate cars: car A and car B. Their distance from home is recorded on the graph.
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 |