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.

Accepted Solution

Answer:Part a) The area of the garden will be [tex]159\frac{4}{9}\ ft^{2}[/tex]Part b) [tex]33\%[/tex]Step-by-step explanation:step 1Find the area of the original gardenThe area is equal to[tex]A=LW[/tex]we have[tex]L=10\ ft[/tex][tex]W=12\ ft[/tex]substitute[tex]A=(10)(12)=120\ ft^{2}[/tex]step 2Find the area of the expanded gardenwe know that[tex]1\frac{2}{3}\ ft=\frac{5}{3}\ ft[/tex]so[tex]L=(10+\frac{5}{3})=\frac{35}{3}\ ft[/tex][tex]W=(12+\frac{5}{3})=\frac{41}{3}\ ft[/tex]The new area is[tex]A=(\frac{35}{3})(\frac{41}{3})=\frac{1,435}{9}\ ft^{2}[/tex]Convert to mixed number[tex]\frac{1,435}{9}\ ft^{2}=\frac{1,431}{9}+\frac{4}{9}=159\frac{4}{9}\ ft^{2}[/tex]step 3Divide the expanded area by the original area[tex](\frac{1,435}{9})/120=1.33[/tex]Convert to percentage[tex]1.33*100=133\%[/tex]thereforeThe percent that the garden has grown is[tex]133\%-100\%=33\%[/tex]