Chapter 8, Problem 1NT

NOW TRY THIS

Noah has some white square tiles and some blue square tiles. They are all the same size. He first makes a row of white tiles and then surrounds the white tiles with a single layer of blue tiles, as shown in Figure $1$.

How many blue tiles does he need:

a. to surround a row of $100$ white tiles?

b. to surround a row of $n$ white tiles?

To determine

(a)

To find:

Number of blue tiles needed to surround hundred white tiles by a single layer of blue tiles.

Answer to Problem 1NT

Solution:

Number of blue tiles needed to surround hundred white tiles is $206$.

Explanation of Solution

Given:

All tiles are of same size. A row of white tiles is surrounded by a single layer of blue tiles.

Approach:

Number of blue tiles needed will be sum of two times number of white tiles and six tiles on the sides.

Calculation:

Number of white tiles $=100$.

Number of blue tiles needed to surround hundred white tiles,

$\begin{array}{l}=2\times 100+2\times 3\\ =200+6\\ =206\end{array}$

Hence, $206$ blue tiles are needed to surround hundred white tiles.

To determine

(b)

To find:

Number of blue tiles needed to surround n white tiles by a single layer of blue tiles.

Answer to Problem 1NT

Solution:

Number of blue tiles needed to surround hundred white tiles is $2n+6$.

Explanation of Solution

Given:

All tiles are of same size. A row of white tiles is surrounded by a single layer of blue tiles.

Approach:

Number of blue tiles needed will be sum of two times number of white tiles and six tiles on the sides.

Calculation:

Number of white tiles $=n$.

Number of blue tiles needed to surround n white tiles,

$\begin{array}{l}=2\times n+2\times 3\\ =2n+6\\ =2n+6\end{array}$

Hence, $2n+6$ blue tiles are needed to surround n white tiles.