Question

The sum of two numbers is 36 and the difference is 10. What are the numbers?Larger number:Smaller number:

Answer 1

23, 13

1) We can solve this problem by setting up a system of equations.

2) We can write out the following and solve it by the Elimination method:

$\begin{gathered} a+b=36 \\ a-b=10 \\ ------- \\ 2a=46 \\ \frac{2a}{2}=\frac{46}{2} \\ a=23 \end{gathered}$

Since a is 23 then we can plug into any of those equations and solve it for b:

$\begin{gathered} a+b=36 \\ 23+b=36 \\ 23-23+b=36-23 \\ b=13 \end{gathered}$

3) Thus, the largest number is 23, and the smallest one is 13