# Margaret wants to paint a rectangular toy box that is 2 ft wide by 1.5 ft high by 4 ft long. One quart of paint will cover 100 ft squared. How many quarts of paint will she need to buy if she puts two coats on both the inside and outside of the toy box?

May 31, 2018

One quart, but she is cutting it close.

#### Explanation:

Disregarding the fact that the walls to the toy box itself will have a width:
The length of the toy box is $4$ feet. Two of the four sides will be this long. Because they will also have height, you multiply the height and length to find the area of one side. Then multiply it by two to count for both sides that will be this long:

$4 \cdot 1.5 = 6$

$6 \cdot 2 = 12$ ${\text{ft}}^{2}$

The same logic applies to the other side:

$2 \cdot 1.5 = 3$

$3 \cdot 2 = 6$ ${\text{ft}}^{2}$

Now, lets add the two numbers together:

$6 + 12 = 18$ ${\text{ft}}^{2}$

To count for the inside of the box as well, multiply it by two:

$18 \cdot 2 = 36$ ${\text{ft}}^{2}$

Since there are two layers of paint, the amount of square feet will be doubled one last time:

$36 \cdot 2 = 72$ ${\text{ft}}^{2}$

So she is using $72$ ${\text{ft}}^{2}$ of the available quart.

But wait, the question wasn't entirely clear. If you meant to color just the walls, that was the correct answer. But to include the floor, well, lets run the numbers. We just need to find the area of the floor of the box, then multiply it by two too count for the other side:

$2 \cdot 4 = 6$

$6 \cdot 2 = 12$ ${\text{ft}}^{2}$

Again, there are two layers, so double this number:

$12 \cdot 2 = 24$ ${\text{ft}}^{2}$

Ok, the real last step is too add the walls to the floors:

$24 + 72 = 96$ ${\text{ft}}^{2}$

So the final answer is $96$ ${\text{ft}}^{2}$ of the paint, or just one can of paint.