Question

The difference between two numbers is 9 and the sum of the number is 31.Find the numbers.

Answer 1

Dear student
$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{numbers}\mathrm{be}\mathrm{x}\left(\mathrm{larger}\mathrm{number}\right)\mathrm{and}\mathrm{y}\left(\mathrm{smaller}\mathrm{number}\right) \\ \mathrm{A}.\mathrm{T}.\mathrm{Q} \\ \mathrm{x}-\mathrm{y}=9 \\ \mathrm{x}+\mathrm{y}=31 \\ \mathrm{Adding}\mathrm{bith}\mathrm{the}\mathrm{equations}\mathrm{we}\mathrm{get} \\ \Rightarrow 2\mathrm{x}=40 \\ \Rightarrow \mathrm{x}=\frac{40}{2}=20 \\ \Rightarrow \boxed{\mathbf{x}\mathbf{=}\mathbf{20}} \\ \mathrm{Hence}\mathrm{y}=31-\mathrm{x} \\ =31-20 \\ =11 \\ \mathrm{So},\boxed{\mathbf{}\mathbf{y}\mathbf{=}\mathbf{11}} \end{gathered}$$
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