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**Hint**: For the first part of the question, we will substitute different values for \[x\] until we get the answer \[4\] for \[3x - 14\] .

For the second part of the question, we will find the cost of one ball pen and pen. Then we will write their ratio in the form of \[\dfrac{a}{b}\] .

**:**

__Complete step-by-step answer__a).In this given problem,

In order to determine the given equation \[3x - 14 = 4\] by hit and trial method.

We will use trial and error (hit and trial) method and substitute different values for \[x\] starting from \[1\] .

Taking, \[x = 1\] , we will get,

\[3(1) - 14 = 4\]

\[ \Rightarrow - 11 \ne 4\]

Since we did not get the correct answer, we have to continue till we equalize both sides of the equation.

Taking \[x = 2\] , we will get,

\[3(2) - 14 = 4\]

\[ \Rightarrow - 8 \ne 4\]

Similarly, check for \[x = 3,4,5,6\] .

Taking, \[x = 6\] , we will get,

\[3(6) - 14 = 4\]

\[18 - 14 = 4\]

\[ \Rightarrow 4 = 4\]

Hence, we get \[x = 6\] by hit and trial method.

b).It is given that the cost of \[8\] ball pens is Rs. \[56\] . So, cost of one ball pen will be-

\[\dfrac{{56}}{8} = Rs.7\]

Similarly, the cost of a dozen pens is Rs. \[180\] . So, cost of one pen will be-

\[\dfrac{{180}}{{12}} = Rs.15\]

Now we can get the ratio of cost of a pen to cost of ball as follows:

\[\dfrac{{15}}{7}\] .

Therefore, Cost of \[8\] ball pens is Rs. \[56\] and the cost of a dozen pens is Rs. \[180\] . \[15:7\] is the ratio of the cost of a pen to the cost of a ball pen.

**So, the correct answer is “ \[15:7\] ”.**

**Note**: The term "trial and error" refers to the process of determining whether or not a particular decision is correct (or wrong). We simply check by substituting that option into the problem. Some questions can only be answered by trial and error; for others, we must first determine whether there isn't a quicker way to find the answer.

For solving the second part of the question, while finding ratios, we should always convert the object to a single unit. We should also note that a dozen means \[12\] quantities. However, a baker’s dozen is \[13\] .

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