Question

Jim’s backyard is a rectangles that is 15 5/6 yards long and 10 2/5 yards wide. Jim buys sod in pieces that are 1 1/3 yards long and 1 1/3 yards wide. How many pieces of sod will Jim need to cover his backyard with sod?

Answer 1

`93\ pieces`

Explanation:

step 1

Find out the area of Jim’s backyard

The area of rectangle is

`A=LW`

we have

`L=15(5)/(6)\ yd=(15*6+5)/(6)=(95)/(6)\ yd` --> convert to an improper fraction

`W=10(2)/(5)\ yd=(10*5+2)/(5)=(52)/(5)\ yd` --> convert to an improper fraction

substitute

`A=((95)/(6))((52)/(5))`

`A=(4,940)/(30)\ yd^2`

Simplify

`A=(494)/(3)\ yd^2`

step 2

Find out the area of one piece of sod

The area of a square is

`A=b^(2)`

we have

`b=1(1)/(3)\ yd=(1*3+1)/(3)=(4)/(3)\ yd` --> convert to an improper fraction

substitute

`A=((4)/(3))^(2)`

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

step 3

we know that

To find out the number of pieces of sod needed, divide the total area of Jim’s backyard by the area of one piece of sod

`(494/3)/(16/9)=(4,446)/(48)\ pieces`

Simplify

`(741)/(8)\ pieces`

Convert to mixed number

`(741)/(8)\ pieces=(736)/(8)+(5)/(8)=92(5)/(8)\ pieces`

Round to the nearest whole number

`93\ pieces`