Question

One-half of a roll of wallpaper covers 1/10th of a wall. How many rolls of wallpaper are needed to cover half the wall? (a) 2/10 (b) 2 1/12 (c) 5 (d) 10

Answer 1

`2(1)/(2)` rolls of the wallpaper will cover half the wall

The correct option is (b) 2 1/2

Explanation:

To determine the number of rolls of wallpaper that are needed to cover half (1/2) the wall,

From the question,

One-half of a roll of wallpaper covers 1/10th of a wall.

Hence, we are to determine the number of rolls of wallpaper that are needed to cover 5/10th of the wall. (NOTE: 5/10th of the wall = 1/2 the wall)

Now,

First, we will find the part of the wall that will be covered by one roll of the wallpaper

If one-half of the roll of wallpaper covers 1/10th of the wall.

Then, one roll (two halves) will cover 2 × 1/10th of the wall

= 1/5th of the wall

Hence one roll will cover 1/5th of the wall

Now, for the number of rolls that will cover half (1/2) the wall

If one roll of the wallpaper covers 1/5th of the wall

Then,
`x` rolls of the wallpaper will cover 1/2 of the wall

`x =(1/2 * 1)/(1/5)`

`x =(5)/(2)`

`x =2(1)/(2)`

Hence,
`2(1)/(2)` rolls of the wallpaper will cover half the wall

Answer 2

2 1/2 rolls

Explanation:

rolls : walls = (1/2) : (1/10) = ? : (1/2) = 5/2 : 1/2 (multiply by 5, since 1/2 = 5/10)

It takes 5/2 rolls = 2 1/2 rolls to cover half the wall.