1. A bathroom measures $$ 10 \frac{1}{2} $$ by $$ 8 \frac{1}{4} $$ feet. New tile costs $$ \$ 12 $$ per square foot. How much will it cost to retile the bathroom?

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UpStudy AI · Accepted Answer

To find the cost of retiling the bathroom, we need to follow these steps:

1. **Calculate the area of the bathroom in square feet.**
2. **Multiply the area by the cost per square foot of the tile.**

### Step 1: Calculate the Area

The dimensions of the bathroom are given as $$ 10 \frac{1}{2} $$ feet and $$ 8 \frac{1}{4} $$ feet. We first convert these mixed numbers into improper fractions.

- For $$ 10 \frac{1}{2} $$:
  $$
  10 \frac{1}{2} = 10 + \frac{1}{2} = \frac{20}{2} + \frac{1}{2} = \frac{21}{2}
  $$

- For $$ 8 \frac{1}{4} $$:
  $$
  8 \frac{1}{4} = 8 + \frac{1}{4} = \frac{32}{4} + \frac{1}{4} = \frac{33}{4}
  $$

Now, we can calculate the area $$ A $$ of the bathroom:
$$
A = \text{length} \times \text{width} = \left(\frac{21}{2}\right) \times \left(\frac{33}{4}\right)
$$

### Step 2: Calculate the Area

Now, let's perform the multiplication:
$$
A = \frac{21 \times 33}{2 \times 4} = \frac{693}{8}
$$

Next, we convert this improper fraction to a decimal to make it easier to work with:
$$
A = 86.625 \text{ square feet}
$$

### Step 3: Calculate the Cost

The cost of tiling is $$ \$12 $$ per square foot. Therefore, the total cost $$ C $$ can be calculated as:
$$
C = A \times \text{cost per square foot} = 86.625 \times 12
$$

Now, let's calculate the total cost.

$$
C = 1039.5
$$

Thus, the total cost to retile the bathroom is $$ \$1039.50 $$.
The cost to retile the bathroom is \$1,039.50.

1. A bathroom measures \( 10 \frac{1}{2} \) by \( 8 \frac{1}{4} \) feet. New tile costs \( \$ 12 \) per square foot. How much will it cost to retile the bathroom?

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