Answer:
[tex]93\ pieces[/tex]
Step-by-step explanation:
step 1
Find out the area of Jim’s backyard
The area of rectangle is
[tex]A=LW[/tex]
we have
[tex]L=15\frac{5}{6}\ yd=\frac{15*6+5}{6}=\frac{95}{6}\ yd[/tex] --> convert to an improper fraction
[tex]W=10\frac{2}{5}\ yd=\frac{10*5+2}{5}=\frac{52}{5}\ yd[/tex] --> convert to an improper fraction
substitute
[tex]A=(\frac{95}{6})(\frac{52}{5})[/tex]
[tex]A=\frac{4,940}{30}\ yd^2[/tex]
Simplify
[tex]A=\frac{494}{3}\ yd^2[/tex]
step 2
Find out the area of one piece of sod
The area of a square is
[tex]A=b^{2}[/tex]
we have
[tex]b=1\frac{1}{3}\ yd=\frac{1*3+1}{3}=\frac{4}{3}\ yd[/tex] --> convert to an improper fraction
substitute
[tex]A=(\frac{4}{3})^{2}[/tex]
[tex]A=\frac{16}{9}\ yd^{2}[/tex]
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
[tex](494/3)/(16/9)=\frac{4,446}{48}\ pieces[/tex]
Simplify
[tex]\frac{741}{8}\ pieces[/tex]
Convert to mixed number
[tex]\frac{741}{8}\ pieces=\frac{736}{8}+\frac{5}{8}=92\frac{5}{8}\ pieces[/tex]
Round to the nearest whole number
[tex]93\ pieces[/tex]
