Question

There are two numbers. The second number is 1 larger than twice the first number. The sum of the reciprocals of the twon numbers is 7/10. What are the two numbers.

Answer 1

There are two numbers.
give a name to one of the numbers. example: call the first number "x"
The second number is 1 larger than twice the first number.
1 larger than twice x
1 plus 2 times x
1+2x

so the two numbers are: x and (1+2x)

The sum of the reciprocals
reciprocal of x means 1/x ("flip" it)
the reciprocal of (1+2x) is 1/(1+2x)
now add these reciprocals (they add up to 7/10)
\[ \frac{1}{x}+\frac{1}{(2x+1)} = \frac{7}{10} \]