Question

One ball pen costs Rs. \[x\] and one fountain pen costs Rs. \[y\]. Find the cost of \[{{y}^{2}}\] ball pens and \[{{x}^{2}}\] fountain pens.

Answer 1

Hint: In this question the variables are already assigned to the cost and number of pens. It is given that we have to find cost of pens when number of pens is specified and also we are given with cost of one pen, so cost of two pens is making that cost twice and similarly for three pens is making that cost thrice and so on we end up with a general formula or relation in the form of variables given in the question.

Complete step-by-step answer:
Let us start with ball pens,
It is given that the cost of one ball pen is Rs. \[x\] and we have to find the cost of \[{{y}^{2}}\] ball pens which is the number of ball pens.
By using the unitary method we can find the cost of as much ball pens as we want,
Cost of 1 ball pen is Rs. \[x\]
Cost of 2 ball pens is Rs. \[2x\]
.
.
.
.
Cost of n ball pens is Rs. \[nx\]
So, now we have arrived at the general formula which is to multiply the specified number of pens with the cost of one pen and you will get the final total cost of the specified number of pens.
Hence, the cost of \[{{y}^{2}}\] number of ball pens is Rs. \[{{y}^{2}}x\].
Now let us move forward to find the cost of fountain pens,
It is given that the cost of one fountain pen is Rs. \[y\] and we have to find the cost of \[{{x}^{2}}\] fountain pens which is the number of fountain pens.
By using the unitary method we can find the cost of as much fountain pens as we want,
Cost of 1 fountain pen is Rs. \[y\]
Cost of 2 fountain pens is Rs. \[2y\]
.
.
.
.
Cost of n fountain pens is Rs. \[ny\]
So, now we have arrived at the general formula which is to multiply the specified number of pens with the cost of one pen and you will get the final total cost of the specified number of pens.
Hence, the cost of \[{{x}^{2}}\] number of fountain pens is Rs. \[{{x}^{2}}y\].
Therefore the total combined cost of ball pens and fountain pens is \[{{x}^{2}}y+{{y}^{2}}x\].

Note: There may be given cost of multiple pens let's say of 3 pens in the questions sometimes, but there is nothing to worry if cost of some specific number of pens is asked then first find the cost of one pen by dividing the cost of 3 pens by 3 and if some specific cost is given and in question it is asked to find the number of pens then find the number of pens we can get from 1 unit currency or Rs. 1, by dividing or multiplying the given relations with some number, and multiply the 1 unit currency with the currency or total cost given in the question and on the opposite side we will get the number of pens we can get with this amount of cost.
Do not get confused on the fact that why we use multiplication and division and not addition and subtraction because cost of one product is same as cost of other same product so by adding one on both sides will be wrong because increasing cost by one and at the same time increasing quantity by one means that the second same product you buy has cost of 1 unit rather than the original cost of the first product buy, so hence we go for multiplication.
To analyze the question with ease or to check the answer you have derived is correct or not just put some numerical values in the relation you have derived and you will know about it.