Question

The difference between two numbers is 9. The first number plus twice the other number is 27. Find the two numbers

Answer 1

15 and 6

Explanation:

`a,\ b-\text{the numbers}\\\\\text{The difference between two numbers is 9}:\ a-b=9\\\text{The first number plus twice the other number is 27}:\ a+2b=27\\\\\text{The system of equations:}\\\\\left\{\begin{array}{ccc}a-b=9\\a+2b=27&\text{change the signs}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}a-b=9\\-a-2b=-27\end{array}\right}\qquad\text{add all sides of the equations}\\.\qquad-3b=-18\qquad\text{divide both sides by (-3)}\\.\qquad\boxed{b=6}`

`\text{Put the value of}\ b\ \text{to the first equation and solve for}\ a:\\\\a-6=9\qquad\text{add 6 to both sides}\\\boxed{a=15}`