Question

a floor having length of 78 feet and width of 52 feet needs to be covered with square tiles of Edge length 31 by 4 feet how many tiles will be needed in all to pay the clone also the boundary tiles need to be coloured blue if one bucket of blue paint can colour 72 by 3 then the find the the number of buckets required​

Answer 1

QUESTION:

A floor, having a length of 78 feet, and a width of 52 feet need to be covered with square tiles of Edge length $3\frac{1}{4}$ feet. How many tiles will be needed in all? Also, the boundary tiles need to be colored blue if one bucket of blue paint can color $7\frac{2}{3}$ tiles then find the number of buckets required​.

ANSWER:

The number of tiles required is 384, and,

the number of buckets required to color all tiles is about 51 buckets.

Given,

A floor has:

length = 78 feet,

width = 52 feet.

A square tile has edge = $3\frac{1}{4}$ feet.

1 bucket can color $7\frac{2}{3}$ tiles.

To find,

Required number of tiles.

Required number of buckets to color all tiles.

Solution,

The length and width (let l and b) of the floor are given as

l = 78 feet,

b = 52 feet.

The area of the floor ($A_f$) can be determined using

$A_f = l \times b$

So,

$A_f = 78 \times 52$

$\implies A_f = 4056$ ft².

Further, the area of a square tile can be given by

$A = s^{2}$

where s is the edge or side of the tile.

Here,

$s=$ $3\frac{1}{4} = \frac{13}{4}$ ft.

So,

$A=(\frac{13}{4} )^{2}$

$\implies A=\frac{169}{16}$ ft².

Let the required number of tiles be 'n'.

Then, it will follow that

n × area of one tile = area of the floor

Thus,

$n \times \frac{169}{16}=4056$

$\implies n =\frac{4056\times 16}{169 }$

$\implies n = 24\times 16$

$\implies n = 384$ tiles.

Now, as the number of tiles 1 bucket can paint $=7\frac{2}{3}=\frac{23}{3}$ tiles.

The number of buckets required to paint 384 tiles will be

$=\frac{384}{\frac{23}{3} }= 50.08$

≈ 51 buckets.

As 50.08 is more than 50, the number of buckets less than 51 may not be sufficient. Thus, we have to consider 51 buckets.

Therefore,

the number of tiles required is 384, and,

the number of buckets required to color all tiles is about 51 buckets.

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