Linear Applications, SMB-007

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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Show Answers Only

`$C = 1500 + 25x`
`60`
`$500`

Show Worked Solution

i.	`text(Fixed C) text(osts)`	`= 650 + 850`
		`= $1500`

`text(Variable C) text(osts) = $25x`

`:.\ $C = 1500 + 25x`

ii.	`text(From the graph)`
	`text(C) text(osts = Income when)\ x = 60`
	`text{(i.e. where graphs intersect)}`

iii. `text(When)\ \ x = 80:`

`text(Income)`	`= 80 xx 50`
	`= $4000`

`$C`	`= 1500 + 25 xx 80`
	`= $3500`

`:.\ text(Profit)`	`= 4000-3500`
	`= $500`