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More Last updated date: 05th Dec 2023
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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. Verified
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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 $\dfrac{a}{b}$ .

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 $13$ .