Questions: A sidewalk alongside a garden at the conservatory is to be 12 3/4' long. Rectangular stone tiles that are each 1 8 1/4' long are used to form the sidewalk. How many tiles are used?

Solution Steps

To determine how many tiles are needed to form the sidewalk, we need to divide the total length of the sidewalk by the length of one tile. This will give us the number of tiles required. Since the lengths are given in mixed numbers, we will first convert them to improper fractions or decimals for easier calculation.

The length of the sidewalk is given as \( 12 \frac{3}{4} \) feet, which can be converted to a decimal: \[ 12 \frac{3}{4} = 12 + 0.75 = 12.75 \text{ feet} \] The length of one tile is given as \( 1 \frac{8}{4} \) feet, which simplifies to: \[ 1 \frac{8}{4} = 1 + 2 = 3 \text{ feet} \]

To find the number of tiles required, we divide the total length of the sidewalk by the length of one tile: \[ \text{Number of tiles} = \frac{12.75}{3} \approx 4.25 \]

Since we cannot use a fraction of a tile, we round up to the nearest whole number: \[ \text{Tiles needed} = \lceil 4.25 \rceil = 5 \]

Final Answer