Chapter 1.1, Problem 32PPE

a.

To determine

Find the pattern of increase in the number of bangles.

Answer to Problem 32PPE

Multiple of $13$ .

Explanation of Solution

Given information:

The table shows the number of bangles a shop gives you per “baker’s dozen”.

  

Calculation:

Here, we will consider the following table:

  $\begin{array}{ll}Baker’sdozen\hfill & Numberofbangles\hfill \\ 1\hfill & 13\hfill \\ 2\hfill & 26\hfill \\ 3\hfill & 39\hfill \\ b\hfill & \mathrm{.....}\hfill \end{array}$

Now, from the above table we can conclude that:

When baker’s dozen is $1$ the number of bangles will become:

  $13\times numberofbangles,wherenumberofbangles=1$

When baker’s dozen is $2$ the number of bangles will become:

  $13\times numberofbangles,wherenumberofbangles=2$

When baker’s dozen is $3$ the number of bangles will become:

  $13\times numberofbangles,wherenumberofbangles=3$

When baker’s dozen is $n$ the number of bangles will become:

  $13\times numberofbangles,wherenumberofbangles=b$

Thus, the algebraic expression is $13b$ .

Now, the pattern of increase in the number of bangles is described as:

For $1$ baker’s dozen, the numbers of bangles are $13$ which is $13\times 1$

For $2$ baker’s dozen, the numbers of bangles are $26$ which is $13\times 2$

For $3$ baker’s dozen, the numbers of bangles are $39$ which is $13\times 3$ …..So on

Hence, the pattern of increase in the number of bangles is multiple of $13$ .

b.

To determine

Find the operation that can be performed on $b$ to find the number of bangles.

Answer to Problem 32PPE

Multiplication operation on $b$ .

Explanation of Solution

Given information:

The table shows the number of bangles a shop gives you per “baker’s dozen”.

  

Calculation:

Here, the operation on $b$ to find the number of bangles is given by:

Now, we will consider the expression to determine the operation on $b$ to calculate the number of bangles $13b$

Thus, the above expression means multiply $13$ with the number $b$ to find the number of bangles.

Hence, multiplication operation on $b$ is performed to find the number of bangles.