Answer
$7$
Work Step by Step
Let $x$ be the number.
The conditions of the problem translate to
\begin{array}{l}\require{cancel}
\dfrac{3+x}{7+2x}=\dfrac{10}{21}
.\end{array}
Using cross-multiplication and the properties of equality, the equation above is equivalent to
\begin{array}{l}\require{cancel}
21(3+x)=10(7+2x)
\\\\
63+21x=70+20x
\\\\
63+21x=70+20x
\\\\
21x-20x=70-63
\\\\
x=7
.\end{array}
Hence the number, $x,$ to be added is $
7
.$
