Question

Jimmy's backyard is rectangle that is 18 5/6 yards long and 10 2/5 yards wide Jim buy sod in pieces that are 1 1/3 yard long and 1 1/3 yards wide how many whole pieces of sod will Jim need to buy to cover his backyard with sod

Answer 1

111 pieces of soda

Explanation:

step 1

Find the area of the rectangular backyard

The area of the rectangular backyard is equal to

`A=LW`

where

`L=18(5)/(6)\ yd=(18*6+5)/(6)=(113)/(6)\ yd`

`W=10(2)/(5)\ yd=(10*5+2)/(5)=(52)/(5)\ yd`

substitute

`A=((113)/(6))((52)/(5))`

`A=(5,876)/(30)\ yd^2`

step 2

Find the area of one piece of sod

The area of the rectangular piece of sod is

`A=LW`

where

`L=1(1)/(3)\ yd=(1*3+1)/(3)=(4)/(3)\ yd`

`W=1(1)/(3)\ yd=(1*3+1)/(3)=(4)/(3)\ yd`

substitute

`A=((4)/(3))^2\\\\A=(16)/(9)\ yd^2`

step 3

Find the pieces of sod needed

To find out how many whole pieces of sod will Jim need to buy to cover his backyard, divide the area of the backyard by the area of one piece of soda

so

`(5,876)/(30) : (16)/(9)=(52,884)/(480)=110.175`

Round up

111 pieces of soda