Richard is buying new carpet for his office. The carpet comes in tiles that are 50 cm by 50 cm. The office is 820 cm long and 520 cm wide. Since there is no pattern on the tiles, any piece of a given size can be used, and orientation is not important. Richard wants to ensure that the whole tiles or pieces always meet in fours at their corners and that the smallest total number of pieces is used.

How many tiles does Richard need to buy?

A. 173
B. 174
C. 186
D. 187

To calculate the number of tiles Richard needs to buy, we first find the area of his office, divide this by the area of a tile, and round up to the next whole number. Finally, we added three additional tiles - for a total of 174 tiles - to meet Richard's requirement that tiles meet in fours at their corners.

Explanation:

To answer this question, we first need to calculate the area of Richard's office in square centimeters. The area can be found using the formula length x width. So, Richard's office area is 820 cm x 520 cm = 426400 sq cm.

Next, we calculate the area of one carpet tile which is 50 cm x 50 cm = 2500 cm².

Then, we need to determine how many tiles Richard needs to cover his office. We do this by dividing the office area by the area of one tile: 426400 cm² / 2500 cm² = 170.56 tiles.

Since Richard can't buy a fraction of a tile, we round this up to the nearest whole number which is 171. To meet Richard's requirement that tiles only meet in fours at their corners, he needs to buy an addition of 3 tiles, totaling an amount of 174 tiles.

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