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9.05 Applications of simultaneous equations

Interactive practice questions

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

Complete the following table of values for various total monthly call times for the two plans:

Call time (in minutes) Total cost for GO SMALL plan Total cost for GO MEDIUM plan
$20$20 $\editable{}$ $\editable{}$
$30$30 $\editable{}$ $\editable{}$
$40$40 $\editable{}$ $\editable{}$
$50$50 $\editable{}$ $\editable{}$
b

Sketch the graph of the two plans.

Loading Graph...
c

Using the graphs, determine how many minutes of calls would need to be made so that the monthly bill costs the same on both plans.

Easy
7min

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.

Easy
5min

Luke purchases $30$30 L of mixed leaded and unleaded petrol solution for mechanic works, which costs him a total of $\$103.20$$103.20. The price of leaded petrol is $\$3.54$$3.54/L, while the price of unleaded petrol is $\$2.94$$2.94/L.

Let $x$x and $y$y be the number of litres of leaded and unleaded petrol that make up the solution respectively.

Easy
5min

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.

Easy
3min
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Outcomes

1.3.3.2

solve practical problems that involve finding the point of intersection of two straight-line graphs, such as determining the break-even point where cost and revenue are represented by linear equations

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