GRAPHS, FUR1 2005 VCAA 6 MC

One afternoon at the beach Mr Smith bought four ice creams and three drinks for his family at a cost of `$21.40`.
Mrs Brown bought five of the same ice creams and two of the same drinks for `$20.80`.
Based on these prices, the cost of one drink is

A. $2.80

B. $2.90

C. $3.00

D. $3.30

E. $3.40

Show Answers Only

`E`

Show Worked Solution

`text(Let I)`	`= text(cost for one ice cream)`
`text(D)`	`= text(cost for one drink)`

`text(Simultaneous equations)`

`text(4I + 3D)`	`= $21.40 \ \ \ …\ text{(i)}`
`text(5I + 2D)`	`= $20.80 \ \ \ …\ text{(ii)}`

`text{(i)} xx 2:`

`text(8I + 6D = $ 42.80 )\ \ \ …\ text{(iii)}`

`text{(ii)} xx 3:`

`text(15I + 6D = $62.40 )\ \ \ …\ text{(iv)}`

`text{(iii) − (ii)}`

`text(15I − 8I)`	`= 62.40 − 42.80`
`text(7I)`	`= 19.6`
`text(I)`	`= 2.8`

`text{Sub I = 2.8 into (i)}`

`4(2.8) + text(3D)`	`= 21.40`
`11.2 +text(3D)`	`= 21.40`
`text(3D)`	`= 10.2`
`text(D)`	`= 3.4`

`:.\ text(One drink costs $3.40)`

`=> E`