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Q55.

Expert-verifiedFound in: Page 348

Book edition
Common Core Edition

Author(s)
Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff

Pages
183 pages

ISBN
9780547587776

**An 18th century Indian version of chess uses a 10 square by 10 square board. On the board shown, the dots represent your opponent’s chess pieces at the start of the game.**

**Copy the board shown. Mark X’s on your side of the board to represent your chess pieces in an arrangement that matches your opponent’s.****What percent of the squares are occupied at the start of the game?****During one game, 75% of the pieces are still on the board. Of the pieces, 14 belong to you. How many pieces belong to your opponent? Explain.**

a. The completed chess board:

** b. 44% **of the squares are occupied on the board.

** c. 19** chess pieces out of the 75% still on the board belongs to the opponent.

The given $10\times 10$ board is a chess board in which the dots represent the opponent’s chess pieces.

Consider the given chess board.

There are 22 dots that represent chess pieces, on the opponent’s side.

Mark 22 ‘*X*’ on the other side in the same way as arranged on the opponent’s side and complete the chess board.

The 22 ‘*X*’ represents chess pieces of the other player.

The completed chess board is shown below.

The given $10\times 10$ board is a chess board in which the dots represent the opponent’s chess pieces.

Consider the board drawn in part (a).

Total number of squares are 100.

Number of squares occupied by chess pieces are $22+22=44$(each side has 22 chess pieces).

$\begin{array}{c}\text{Percent of squares occupied}=\frac{\text{number of squares occupied}}{\text{total number of squares}}\cdot 100\\ =\frac{44}{100}\cdot 100\\ =44\%\end{array}$

Percent of squares occupied on the board is $44\%$.

$75\%$ of the chess pieces are still on the board.

Number of chess pieces out of $75\%$ that belongs to you are 14.

Number of chess pieces that were on the board primarily are 44.

$75\%$ of the chess pieces are still on the board.

Number of chest pieces still on the board are,

$\begin{array}{c}75\%\cdot 44=\frac{75}{100}\cdot 44\text{[write percent as fraction]}\\ \text{= 33 [simplify]}\end{array}$.

Number of chess pieces out of $75\%$ that belongs to you are 14.

Therefore, number of chest pieces that belong to the opponent are $\text{33}-\text{14}=\text{19}$.

19 chess pieces out of the $75\%$ still on the board belongs to the opponent.

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