Question

5 pointsLuke has budgeted to spend three times more on food thanentertainment. He also wants to spend three times more on rent thanfood. If Luke has $586.04 to spend, what is the most he can spend onfood?

Answer 1

Let us call the food budget f, the entertainment budget e, and the rent budget r. We know the following about Luke's budget

`f=3e`
`r=3f`

and

`r+f+e=586.04`

which can also be written as (since f =3e, its also true that e = f/3)

`3f+f+(f)/(3)=586.04`

we add all the f terms on the left to get

`(3+1+(1)/(3))f=586.04`
`(4+(1)/(3))f=586.04`
`((12)/(3)+(1)/(3))f=586.04`

`(13f)/(3)=586.04`
`\textcolor{#FF7968}{\therefore f=135.24}`

Hence, the maximum luke can spend on food is $135.24.