MATH SOLVE

4 months ago

Q:
# Select ALL the correct answers.Members of the service club at Rebecca's school must spend a minimum of 20 hours doing volunteer work each semester. The number of hours spent volunteering at school activities can be no more than twice the number of hours spent volunteering outside of school.When x represents the number of hours spent volunteering in school and y represents the number of hours spent volunteering outside of school, this situation can be modeled by a system of inequalities.Which ordered pairs represent solutions to the system?(7,11)(15,6)(8,16)(12,5)(0,22)(10,10)

Accepted Solution

A:

Answer:(8,16) (0,22) (10,10)Step-by-step explanation:Let x represents the number of hours spent volunteering in school and y represents the number of hours spent volunteering outside of school. Since each member must spend a minimum of 20 hours doing volunteer work each semester.The equation forms : [tex]x+y\geq 20[/tex] ....(1)Also given is that the number of hours spent volunteering at school activities can be no more than twice the number of hours spent volunteering outside of school, then equation becomes:[tex]x\leq 2y[/tex] .....(2)So, lets check with each given pair, if they fulfill both equations:(7,11): [tex]7+11=18[/tex] is not ≥ 20 - This is false.(15,6): [tex]15 \leq 6(2)[/tex] = 12 - This is false.(8,16): [tex]8+16=24[/tex] which is ≥20 and [tex]8 \leq 2(16)=32[/tex] - This is true.(12,5): 12 is not ≤ [tex]2(5)=10[/tex] - This is false.(0,22): [tex]0+22\geq 20[/tex] and [tex]0\leq 2(22)=44[/tex] - This is true.(10,10): [tex]10+10\geq 20[/tex] and [tex]10\leq 2(10)=20[/tex]- This is true.