Ita publishes and sells calendars for $25 each. The cost of producing the calendars is $8 each plus a set up cost of $5950.
How many calendars does Ita need to sell to breakeven? (2 marks)
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Algebra, STD2 A4 2005 HSC 28b
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 $12 per person.
- Write a formula for the cost ($C) of running the dance for `x` people. (1 mark)
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The graph shows planned income and costs when the ticket price is $20.
- Estimate the minimum number of people needed at the dance to cover the costs. (1 mark)
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- How much profit will be made if 150 people attend the dance? (1 mark)
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Sue and Mikey plan to sell 200 tickets. They want to make a profit of $1500.
- What should be the price of a ticket, assuming all 200 tickets will be sold? (3 marks)
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Algebra, STD2 A4 EQ-Bank 20
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 $25 per person.
- Write a formula for the cost ($C) of holding the charity event for `x` people. (1 mark)
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- The graph below shows the planned income and costs if they charge $50 per ticket. Estimate the number of guests they need to break even. (1 mark)
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- How much profit will Fiona and John make if 80 people attend their event? (1 mark)
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Algebra, STD2 A2 2007 HSC 27b
A clubhouse uses four long-life light globes for five hours every night of the year. The purchase price of each light globe is $6.00 and they each cost `$d` per hour to run.
- Write an equation for the total cost (`$c`) of purchasing and running these four light globes for one year in terms of `d`. (2 marks)
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- Find the value of `d` (correct to three decimal places) if the total cost of running these four light globes for one year is $250. (1 mark)
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- If the use of the light globes increases to ten hours per night every night of the year, does the total cost double? Justify your answer with appropriate calculations. (1 mark)
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- The manufacturer’s specifications state that the expected life of the light globes is normally distributed with a standard deviation of 170 hours.
What is the mean life, in hours, of these light globes if 97.5% will last up to 5000 hours? (1 mark)
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Show Worked Solution
a. `text(Purchase price) = 4 xx 6 = $24`
| `text(Running cost)` | `= text(# Hours) xx text(Cost per hour)` |
| `= 4 xx 5 xx 365 xx d= 7300d` |
`:.\ $c = 24 + 7300d`
b. `text(Given)\ \ $c = $250:`
| `250` | `= 24 + 7300d` |
| `7300d` | `= 226` |
| `d` | `= 226/7300= 0.03095…= 0.031\ $ text(/hr)\ text{(3 d.p.)}` |
c. `text(If)\ d\ text(doubles to 0.062)\ \ $text(/hr)`
`$c= 24 + 7300 xx 0.062= $476.60`
`text(S) text(ince $476.60 is less than)\ 2 xx $250\ ($500),`
`text(the total cost increases to less than double)`
`text(the original cost.)`
d. `sigma = 170`
`z\ text(-score of 5000 hours) = 2`
| `z` | `= (x-mu)/sigma` |
| `2` | `= (5000-mu)/170` |
| `340` | `= 5000-mu` |
| `mu` | `= 4660` |
`:.\ text(The mean life of these globes is 4660 hours.)`
Algebra, STD2 A4 2011 HSC 20 MC
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?
- `$15\ 000`
- `$20\ 000`
- `$30\ 000`
- `$40\ 000`