How do you define a variable and write an expression for each phrase: the sum of 13 and twice a number?

Hint: To solve such question we should have general understanding of the language used for the mathematical expressions, the mathematical expression is converted into statement by using the words related to the sign, like for multiplication “of” is used, for addition “sum” is used.

Complete step by step solution:
Here the given question is to derive the mathematical expressions for the given statements, on assuming the variable and converting it to the mathematical expression we get:
The first statement is:
The sum of “13”, lets the variables be “x” and ”y”, now we get:
\[ \Rightarrow x + y = 13\]
Now the second statement given in the question is:
An twice a number, for this let us say the variable is “z” and the number is “10”
Converting it to mathematical expression we get:
\[\Rightarrow 2(z) = 100 \\
\therefore z = \dfrac{{100}}{2} = 50 \]

Note: The conversion of statement to the algebraic equation needs only the understanding of the statement, you should be careful about the words written over there and accordingly you can re-write it in the terms of math’s. For example “of” is used for product, “ratio” is used for division, “sum” is used for addition and “difference” is used for subtraction.Here in this question two separate phrases were given hence two equations are obtained, if asked for the relation between the two phrases then we can also find that relation.