1. A certain ceiling is made up of tiles. Every square meter of ceiling requires 10.75 tiles. Fill in the table with the missing values. square meters of ceiling number of tiles 1 1 10 100 a

The missing values in the table have been calculated and they are underlined below;

1) 1 m² = 10.75 tiles

2) 10 m² = 107.5 tiles

3) 9.3 m² of tiles = 100 tiles

4) a m² = 10.5a tiles

The table is missing and so i have attached it.

From the question, we are told that each square meter of ceiling requires 10.75 tiles. Thus on the first row;

1 m² = 10.75 tiles

The second row of the table shows 10 m² of tiles.

Thus, by proportion, 10 m² of tiles will require; 10 × 10.75 tiles = 107.5 tiles

The third row shows us 100 tiles required.

Since 10.75 tiles is for 1  m² , then by proportion, we can find the square meters of tiling of 100 tiles. Thus;

100 tiles will use; 100 × 1/10.75 = 9.3 m² of tiles

The fourth row shows us square meter of tiles to be a.

Thus by proportion, number of tiles required for this square meter of tile is;

a × 10.75/1 = 10.75a tiles

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Given:

Consider the below table attached with this question.

Every square meter of ceiling requires 10.75 tiles.

To find:

The missing values in the table.

Solution:

We have,

1 square meter of ceiling =  10.75 tiles.      ...(i)

Therefore, the number of tiles corresponding to 1 square meter of ceiling is 10.75.

Multiply both sides by 10.

10×1 square meter of ceiling =  10×10.75 tiles.

10 square meter of ceiling =  107.5 tiles.

Therefore, the number of tiles corresponding to 10 square meter of ceiling is 107.5.

Divide both sides by 10.75 in (i).

square meter of ceiling = 1 tile.

Multiply both sides by 100.

square meter of ceiling = 100 tiles.

On approximating the value, we get

9.3 square meter of ceiling = 100 tiles.

Therefore, the square meters of ceiling corresponding to 100 tiles is about 9.3.

Multiply both sides by a in (i).

a×1 square meter of ceiling =  a×10.75 tiles.

a square meter of ceiling =  10.75a tiles.

Therefore, the number of tiles corresponding to a square meter of ceiling is 10.75a.