# Problem of the Week Problem B and Solution Jafarâ€™s New Floor

## Problem

Jafar is laying new hardwood flooring in his rectangular living room, which has an area of $$66~\text{m}^2$$. Each box of flooring has $$8$$ identical wooden planks, and each plank has an area of $$0.2~\text{m}^2$$.

1. Assuming that there is no waste, how many planks will he need to cover the floor of his living room?

2. If Jafar wants to buy an extra $$10\%$$ for waste, how many boxes of flooring does he need to buy?

3. If each box costs $$\74.50$$ and sales tax is $$15\%$$, what will be the total cost of the flooring in part (b)?

## Solution

1. The area of the living room floor is $$66~\text{m}^2$$ and each plank has an area of $$0.2~\text{m}^2$$. So the total number of planks needed is $$66 \div 0.2 = 330$$.

2. The extra amount is $$10\%$$ of $$330$$, which is $$0.10 \times 330=33$$ planks.

So in total Jafar wants to buy $$330+33 = 363$$ planks. Since there are $$8$$ planks in each box, the number of boxes required is $$363 \div 8 = 45.375$$. Therefore, he should buy $$46$$ boxes.

3. Jafar wants to buy $$46$$ boxes, and each box costs $$\74.50$$. The total cost before tax is $$46 \times \74.50 = \3427$$.

The amount of tax is $$15\%$$ of $$\3427$$, which is $$0.15 \times \3427 = \514.05$$.

Therefore, the total cost of the flooring is $$\3427 + \514.05 = \3941.05$$.