Answer: Gianna worked 6 hours and Matthew worked 5 hours.
Step-by-step explanation:
Let be "g" the number of hours Gianna worked and "m" the number of hours that Matthew worked.
Using the information given in the exercise, set up a System of equations:
[tex]\left \{ {{g+m=11} \atop {30g+10m=230}} \right.[/tex]
You can use the Elimination Method to solve the System of equations:
1. You can multiply the first equation by -10.
2. Then you must add both equations.
3. You must solve for "g".
Then:
[tex]\left \{ {{-10g-10m=-110} \atop {30g+10m=230}} \right.\\..........................\\20g=120\\\\g=\frac{120}{20}\\\\g=6[/tex]
4. Finally, you need to substute the value of "g" into any original equation and solve for "m" in order to find its value:
[tex]g+m=11\\\\6+m=11\\\\m=11-6\\\\m=5[/tex]
