Question

aunt jane has a vegetable garden that is 10 feet long and 12 feet wide. she wants to expand the garden next year to be able to grow more vegetables, so she plans to extend the length and width each by 1 2/3 feet. what will the area of next years garden be? by what percent with the garden have grown? round to the nearest whole number percent.

Answer 1

Part a) The area of the garden will be
`159(4)/(9)\ ft^(2)`

Part b)
`33\%`

Explanation:

step 1

Find the area of the original garden

The area is equal to

`A=LW`

we have

`L=10\ ft`

`W=12\ ft`

substitute

`A=(10)(12)=120\ ft^(2)`

step 2

Find the area of the expanded garden

we know that

`1(2)/(3)\ ft=(5)/(3)\ ft`

so

`L=(10+(5)/(3))=(35)/(3)\ ft`

`W=(12+(5)/(3))=(41)/(3)\ ft`

The new area is

`A=((35)/(3))((41)/(3))=(1,435)/(9)\ ft^(2)`

Convert to mixed number

`(1,435)/(9)\ ft^(2)=(1,431)/(9)+(4)/(9)=159(4)/(9)\ ft^(2)`

step 3

Divide the expanded area by the original area

`((1,435)/(9))/120=1.33`

Convert to percentage

`1.33*100=133\%`

therefore

The percent that the garden has grown is

`133\%-100\%=33\%`