Chapter 1.2, Problem 30IP

To determine

Write and evaluate an expression to find how many total tiles are needed if there are 15 red tiles, then make a table showing the total number of tiles if there are 15, 20, 25, or 30 red tiles.

Answer to Problem 30IP

  $\text{T}=\text{R}+12\text{R}$

  $\text{T}=195\text{tiles}$

Red	Total tiles
15	195
20	260
25	325
30	390

Explanation of Solution

GIVEN:

A decorative floor pattern has 1 red square tile surrounded by 12 blue tiles.

In order to write and evaluate an expression to find how many total tiles are needed if there are 15 red tiles, first let the number of total tiles be T and number of red tiles be R and the number of blue tiles is the product of the number of red tiles and 12, every red tile is surrounded by 12 blue tiles so, the expression is total tiles is equal to the sum of the number of red tiles and the product of 12 and number of red tiles as shown below:

  $\text{T}=\text{R}+12\text{R}$

Now, putting the number of red tiles, that is 15 in the above expression and solving it as shown below:

  $\begin{array}{l}\text{T}=\text{R}+12\text{R}\\ \text{T}=15+12\times 15\\ \text{T}=15+180\\ \text{T}=195\end{array}$

So, the number of total tiles are needed if there are 15 red tiles is 195 tiles.

Now, in order to make a table showing the total number of tiles if there are 15, 20, 25, or 30 red tiles.

First for 20 red tiles, putting the value of red tile in the expression $\text{T}=\text{R}+12\text{R}$ so total tiles will be :

  $\begin{array}{l}\text{T}=\text{R}+12\text{R}\\ \text{T}=20+12\times 20\\ \text{T}=20+240\\ \text{T}=260\end{array}$

Then for 25 red tiles, putting the value of red tile in the expression $\text{T}=\text{R}+12\text{R}$ so total tiles will be :

  $\begin{array}{l}\text{T}=\text{R}+12\text{R}\\ \text{T}=25+12\times 25\\ \text{T}=25+300\\ \text{T}=325\end{array}$

And then for 30 red tiles, putting the value of red tile in the expression $\text{T}=\text{R}+12\text{R}$ so total tiles will be :

  $\begin{array}{l}\text{T}=\text{R}+12\text{R}\\ \text{T}=30+12\times 30\\ \text{T}=25+360\\ \text{T}=390\end{array}$

So, the table is as shown below:

Red	Total tiles
15	195
20	260
25	325
30	390