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a) Solve the equation by hit and trial method: \[3x - 14 = 4\]
b) Cost of \[8\] ball pens is Rs. \[56\] and the cost of a dozen pens is Rs. \[180\] . Find the ratio of the cost of a pen to the cost of a ball pen.

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Last updated date: 13th Jul 2024
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Answer
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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 \[13\] .