Question

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?
(8,16)
(12,5)
(10,10)
(7,11)
(15,6)
(0,22)

Explanation:

Step1: Analyze the first inequality \(x + y \geq 20\)

For each ordered pair \((x,y)\), check if \(x + y\) is at least 20.

• \((8,16)\): \(8 + 16 = 24 \geq 20\)
• \((12,5)\): \(12 + 5 = 17 < 20\)
• \((10,10)\): \(10 + 10 = 20 \geq 20\)
• \((7,11)\): \(7 + 11 = 18 < 20\)
• \((15,6)\): \(15 + 6 = 21 \geq 20\)
• \((0,22)\): \(0 + 22 = 22 \geq 20\)

Step2: Analyze the second inequality \(x \leq 2y\)

For the pairs that passed Step 1, check if \(x \leq 2y\).

• \((8,16)\): \(8 \leq 2\times16 = 32\) (True)
• \((10,10)\): \(10 \leq 2\times10 = 20\) (True)
• \((15,6)\): \(15 \leq 2\times6 = 12\) (False)
• \((0,22)\): \(0 \leq 2\times22 = 44\) (True)

Answer:

(8,16), (10,10), (0,22)