Question

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.

Answer 1

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 $${\displaystyle \frac{a}{b}}$$ .

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-
 $${\displaystyle \frac{56}{8}}=Rs.7$$
Similarly, the cost of a dozen pens is Rs. $$180$$ . So, cost of one pen will be-
 $${\displaystyle \frac{180}{12}}=Rs.15$$
Now we can get the ratio of cost of a pen to cost of ball as follows:
 $${\displaystyle \frac{15}{7}}$$ .
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 $$13$$ .