Aussie Maths & Science Teachers: Save your time with SmarterEd
Year 11 is making pizzas to raise money for a charity.
The cost \((C)\) and revenue \((R)\) in dollars, when \(x\) pizzas are sold are represented by the equations
\begin{aligned}
& C=2.5 x+6 \\
& R=8 x
\end{aligned}
Enough pizzas are sold so that a profit is made.
By how much does the profit increase for each additional pizza sold?
A small business makes and sells bird houses.
Technology was used to draw straight-line graphs to represent the cost of making the bird houses `(C)` and the revenue from selling bird houses `(R)`. The `x`-axis displays the number of bird houses and the `y`-axis displays the cost/revenue in dollars.
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The graph displays the cost (`$c`) charged by two companies for the hire of a minibus for `x` hours.
Both companies charge $360 for the hire of a minibus for 3 hours.
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Write a formula, in the form of `c = mx + b`, for the cost of hiring a minibus from Company B for `x` hours. (2 marks)
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Calculate how much cheaper this is than hiring from Company A. (2 marks)
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Penny is a baker and makes meat pies every day.
The cost of making `p` pies, `$C`, can be calculated using the equation
`C = 675 + 3.5 p`
Penny sells the pies for $5.75 each, and her income is calculated using the equation
`I = 5.75 p`
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a. & b.
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b. `text(Loss zone occurs when)\ C > I,\ text(which is shaded in the diagram above.)`
A charity seeks to raise money by telephoning people at random from a call centre and asking them to donate.
Over the years, this charity has found that the amount of money raised `($A)` is related to the number of telephone calls made `(n)`. A graph of this relationship is shown.
It costs the charity $2100 per week to run the call centre. It also costs an average of 50 cents per telephone call.
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a. `C = $2100 + $0.50n`
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`text(From the above graph, the charity needs to)`
`text(make 700 calls to break even.)`
Sue and Mikey are planning a fund-raising dance. They can hire a hall for $400 and a band for $300. Refreshments will cost them $12 per person.
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The graph shows planned income and costs when the ticket price is $20.
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Sue and Mikey plan to sell 200 tickets. They want to make a profit of $1500.
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Fiona and John are planning to hold a fund-raising event for cancer research. They can hire a function room for $650 and a band for $850. Drinks will cost them $25 per person.
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A function centre hosts events for up to 500 people. The cost `C`, in dollars, for the centre
to host an event, where `x` people attend, is given by:
`C = 10\ 000 + 50x`
The centre charges $100 per person. Its income `I`, in dollars, is given by:
`I = 100x`
How much greater is the income of the function centre when 500 people attend an event, than its income at the breakeven point?
Ashley makes picture frames as part of her business. To calculate the cost, `C`, in dollars, of making `x` frames, she uses the equation `C=40+10x`.
She sells the frames for $20 each and determines her income, `I`, in dollars, using the equation `I=20x`.
Use the graph to solve the two equations simultaneously for `x` and explain the significance of this solution for Ashley's business. (2 marks)
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