Chapter 1.1, Problem 30PPS

To determine

To Evaluate:an expression of having total number of tiles and to make a table showing the total number of tiles

Answer to Problem 30PPS

The expression for the total number of tiles is given by $15+\left(12\times 15\right)$

Number of Tiles	Expression	Evaluation	Total number of tiles
15	$15+\left(12\times 15\right)$	$15+180=195$	$195$
20	$20+\left(12\times 20\right)$	$20+240=260$	$260$
25	$25+\left(12\times 25\right)$	$25+300=325$	$325$
30	$30+\left(12\times 30\right)$	$30+360=390$	$390$

Explanation of Solution

Given:

one red square tile surrounded by 12blue tiles.

there are 15, 20, 25 or 30 red tiles.

  

Calculation:

In this question, write the numerical expression for the following:

Since, each red square tile is surrounded by 12 blue tiles; therefore the 15 red squares will be surrounded by 12x15 blue tiles.

Thus total number of tiles = total red tiles + total blue tiles

The expression for the total number of tiles is given by $15+\left(12\times 15\right)$

Now, evaluate this expression to find the total number of tiles if there are 15 red tiles.

  $15+\left(12\times 15\right)$

Now, to evaluate this expression, follow the order of operations. According to it,first solve the bracket.

  $15+\left(12\times 15\right)=15+180$

Now, perform the addition

  $15+\left(12\times 15\right)=15+180=195$

The total number of tiles if there are 15 red tiles = 195 tiles

Now, make a table showing the total number of tiles if there are for 15, 20, 25, and 30 red tiles.

The expressions for any number of tiles will be like that of for 15 red tiles except that will replace 15 by 20, 25 or 30 as required.

Number of Tiles	Expression	Evaluation	Total number of tiles
15	$15+\left(12\times 15\right)$	$15+180=195$	$195$
20	$20+\left(12\times 20\right)$	$20+240=260$	$260$
25	$25+\left(12\times 25\right)$	$25+300=325$	$325$
30	$30+\left(12\times 30\right)$	$30+360=390$	$390$

Conclusion:

The expression for the total number of tiles is given by $15+\left(12\times 15\right)$