Question

what could the variable ( x ) and inequality reasonably represent?
choose two.

• the variable ( x ) could represent the number of hours in one day that braxton played video games, with ( 7x ) and 210 representing number of hours in one week that braxton played video games.
• the variable ( x ) could represent the number of minutes in one day that braxton spent on homework, with ( 7x ) and 210 representing number of minutes in one week that braxton spent on homework.
• the variable ( x ) could represent the total cost that braxton paid for a new computer with accessories if he paid at least $210 each month for seven months.
• the variable ( x ) could represent the weekly cost of a blog membership that has an annual cost of $210.
• the variable ( x ) could represent the amount of money that braxton and six other friends each had to pitch in to rent a bouncy house with a minimum rental cost of $210.

Explanation:

1. For the first option: A day has 24 hours, so the number of hours in a day playing video games (z) can't realistically be such that 7z = 210 (since 210/7 = 30, which is more than 24). So this is not reasonable.
2. For the second option: If z is the number of minutes per day on homework, 7z would be minutes per week. 210 minutes per week is reasonable (210/7 = 30 minutes per day), so this is reasonable.
3. For the third option: If he pays at least $210 per month for 7 months, the total cost would be at least 7*210, not 7z = 210. So this is not reasonable.
4. For the fourth option: An annual cost of $210, weekly cost z would mean 52z ≈ 210 (not 7z), so this is not reasonable.
5. For the fifth option: Braxton and 6 friends make 7 people. If the minimum rental cost is $210, then 7z ≥ 210 (or 7z = 210 for exact), which is reasonable as z would be the amount each pays.

Answer:

B. The variable \( x \) could represent the number of minutes in one day that Braxton spent on homework, with \( 7x \) and 210 representing number of minutes in one week that Braxton spent on homework.
E. The variable \( x \) could represent the amount of money that Braxton and six other friends each had to pitch in to rent a bouncy house with a minimum rental cost of $210.