Question

The length of a sidewalk is $1$ yard. $\frac{15}{17}$ yards of the sidewalk is fenced with colorful ribbons on the sides. $\frac{5}{17}$ yards of one side of the sidewalk is fenced with blue ribbons and $\frac{3}{17}$ yards is fenced with red ribbons. What length of green ribbon will be required to fence the remaining part of the sidewalk on both sides?

• A. $\frac{2}{17}\text{yd}$
• B. $\frac{9}{17}\text{yd}$
• C. $\frac{14}{17}\text{yd}$
• D. $\frac{7}{17}\text{yd}$

Answer 1

The correct option is C $\frac{14}{17}\text{yd}$


Length of the sidewalk fenced with blue and red ribbons $=\frac{5}{17}+\frac{3}{17}=\frac{5+3}{17}=\frac{8}{17}\text{yd}$
Length of the sidewalk to be fenced with green ribbons on one side $=\frac{15}{17}-\frac{8}{17}=\frac{15-8}{17}=\frac{7}{17}$
Since the green ribbon is to be used on both sides of the sidewalk,
Length of green ribbon required $=\frac{7}{17}+\frac{7}{17}=\frac{7+7}{17}=\frac{14}{17}\text{yd}$

$\therefore \frac{14}{17}\text{yd}$ of green ribbon to fence the remaining part of the sidewalk on both sides.