GRAPHS, FUR1 2004 VCAA 6 MC

The cost, `$C`, of hiring a boat for `x` hours is given by the equation `C = ax + b` where `a` is the hourly rate and `b` is a fixed booking fee.
When the boat is hired for `4` hours the cost is `$320`.
When the boat is hired for `6` hours the cost is `$450`.
When the boat is hired for one hour the cost is

A. $65

B. $75

C. $77

D. $80

E. $125

Show Answers Only

`E`

Show Worked Solution

`C = ax + b\ \ \ …\ text{(i)}`

`a = text(hourly rate)`

`b = text(fixed booking fee)`

`text(Sub)\ x = 4, c = 320\ text{into (i)}`

`320`	`= a(4) + b`
`4a + b`	`= 320 \ \ \ … \ text{(ii)}`

`text(Sub)\ x = 6, c = 450\ text{into (ii)}`

`450 `	`= a(6) + b`
`6a + b`	`= 450 \ \ \ … \ text{(iii)}`

`text{(iii) − (ii)}`

`2a`	`= 130`
`:.\ a`	`= 65`

`text(Sub)\ a = 65\ text{into (ii)}`

`4(65) + b`	`= 320`
`b`	`= 320 − 260`
`b`	`= 60`

`:.\ c = 65x + 60 \ \ \ …\ text{(iv)}`

`text(Sub)\ x = 1\ text{into (iv)}`

`c`	`= 65(1) + 60`
	`= 125`

`:.\ text(C)text(ost is $125 for 1 hr)`

`=> E`