Question

Each quarter of quarters and nickels is worth $ Rs3.70$. There are $22$coins in all of them?

Answer 1

Hint: First of all here we will assume the number of nickel and quarters and then we will frame the mathematical expression using it. There will be two mathematical expressions and two unknowns so I will use elimination method to find out the unknown terms.

Complete step by step answer:
Let us assume that the number of nickels be “n” and the number of quarters be “q”
Now, we are given that there is total $22$coins
$ \Rightarrow n + q = 22$ ….. (A)
Also, given that Each are of quarters and nickels is worth $ Rs3.70$.
$ \Rightarrow 0.05n + 0.25q = 3.70$ ….(B)
Using the equation (A),
$n = 22 - q$
Place the above value in equation –
$ \Rightarrow 0.05(22 - q) + 0.25q = 3.70$
Simplify the above equation –
$1.1 - 0.05q + 0.25q = 3.7$
Arrange the like terms together. Also, when you move any term from one side to another then the sign of the terms also changes. Positive terms become negative and the negative term becomes positive.
$ - 0.05q + 0.25q = 3.7 - 1.1$
Simplify the above equation –
$0.20q = 2.6$
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
$ \Rightarrow q = \dfrac{{2.6}}{{0.2}}$
Simplify the above expression –
$q = 13$ ….. C
Place the above value in equation (A)
$n + 13 = 22$
Move constant on the opposite side –
$
   \Rightarrow n = 22 - 13 \\
   \Rightarrow n = 9 \\
 $
Hence, there are $9$ nickels and $13$ quarters.

Note: Always remember that when you move any term from one side to another then the sign of the term also changes.
Be careful about the sign while doing simplification remember the golden rules-
Addition of two positive terms gives the positive term
Addition of one negative and positive term, you have to do subtraction and give sign of bigger number whether positive or negative.