Percentage and numeric relations I would like to know the simplest approach to the followings:
Que 1:
One student scored $14$ marks more than the other and his marks were $60$% of the sum of their marks. Find marks obtained by them.
My Approach:
Step 1: Assuming students scored $x$ and $x+14$.
Step 2: $x+14$ is $60$% of sum of their marks i.e. $2x+14$, so $x$ is $40$%.
Don't know further.
Ans: 28 and 42 I know the answer but don't know how to achieve. 
 
Que 2:
Two persons are paid total $9.2$ Dollars per week.  $1st$  is paid $260$% more than amount paid to $2nd$. Find their payment for week.
Ans: 2 and 7.2 I know the answer but don't know how to achieve. 
 A: First question:
You are correct, $x$ is $40\%$ of the sum of their marks, and the sum of their marks is $2x+14$.
Now, you need to transform that into an equation.
In general, if $a$ is equal to $p\%$ of $b$ (for example, if "my height" is equal to $90\%$ of "your height"), you know that the ratio between $a$ and $b$, multiplied by $100$, is equal to $p$ (i.e., my height, divided by your height, times $100$, is $90$).
Now, answer these questions (in that order):


*

*how would you write the relation "ratio between $a$ and $b$, multiplied by $100$, is equal to $p$" as an equation?

*In your case, what is $a$ and what is $b$, and what is $p$?

*So in your case, what equation do you get?

*How do you solve this equation?



Second question:
Say the first person is paid $x$, and the second one is paid $y$. Then, transform the following two statements into equations:


*

*They are paid $9.2$ dollars in total.

*The pay of the first person is $260\%$ more than the pay of the second person.


What equations do you get?
A: A percentage is just a different way of writing a number.
People do not like to say things like $0.4$, so instead they
multiply the number by $100$ and attach a percentage sign to it.
That is, by definition,
$$ 0.4 = 40\%.$$
People find it much more agreeable to say $40\%$ than to say $0.4$.
They also prefer very much to say "$40\%$ of something" rather than
"$40\%$ times something", although if you regard $40\%$ as a number
(as I do) then the two phrases mean the same thing.
This is all fine
until it comes time to actually do some arithmetic on the number.
Then I personally find that usually the first thing I would like to do is
to write $40\%$ as $0.4$, and say "times" rather than "of",
and then never think about percentages again.
So for the first problem you found the following:


*

*The sum of the marks is $2x + 14$.

*$x$ is $0.4$ times the sum of the marks


If you introduce a symbol such as $s$ to represent "the sum of the marks", from the two statements above you can derive two equations which are easy
to solve for $x$.
For the second problem, when people say something like "$x$ is $10\%$ more than $y$", they mean that $x$ is $y$ plus another $0.1$ times $y$, or
$x = y + 0.1y = 1.1y$.
That is, "$10\%$ more than" is a way people like to say "$1.1$ times",
"$20\%$ more than" is a way people like to say "$1.2$ times",
"$50\%$ more than" is a way people like to say "$1.5$ times",
and so forth.
So what does "$260\%$ more than" mean?
Now if $x$ is the wages of the lesser-paid worker, and the other
worker is paid $260\%$ more than $x$, and the two wages add up to $9.2$,
you can write a single easily-solved equation with one unknown $x$.
