Let be "x" and "y" the numbers you must find.
You need to remember that:
- A Sum is the result of an Addition.
- "Times" indicates a Multiplication.
- "Less" indicates a Subtraction.
Then, "The sum of two numbers is thirty" can be represented with the following equation:
[tex]x+y=30[/tex]And "One number is five times the other less six" can be represented with the following equation:
[tex]x=5y-6[/tex]Now you can set up the following System of Equations:
[tex]\begin{cases}x+y=30 \\ x=5y-6\end{cases}[/tex]You can solve it by applying the Substitution Method:
1. Substitute the second equation into the first one.
2. Solve for "y".
Then:
[tex]\begin{gathered} (5y-6)+y=30 \\ 6y-6=30 \\ 6y=30+6 \\ \\ y=\frac{36}{6} \\ \\ y=6 \end{gathered}[/tex]3. Substitute the value of "y" into the second equation and evaluate, in order to find the value of "x":
[tex]\begin{gathered} x=5y-6 \\ x=(5)(6)-6 \\ x=30-6 \\ x=24 \end{gathered}[/tex]Therefore, the answer is:
[tex]\begin{gathered} 24\text{ and }6 \\ \end{gathered}[/tex]