a teacher has a 2 - gallon (32 - cup) container of juice. she gives each student $\frac{1}{2}$ cup of juice…

a teacher has a 2 - gallon (32 - cup) container of juice. she gives each student $\frac{1}{2}$ cup of juice. which equation represents the amount of juice that remains, y, after x students are served?\n$y = 32x-\frac{1}{2}$\n$y=\frac{1}{2}x - 32$\n$y=-\frac{1}{2}x + 32$\n$y=-32x+\frac{1}{2}$

a teacher has a 2 - gallon (32 - cup) container of juice. she gives each student $\frac{1}{2}$ cup of juice. which equation represents the amount of juice that remains, y, after x students are served?\n$y = 32x-\frac{1}{2}$\n$y=\frac{1}{2}x - 32$\n$y=-\frac{1}{2}x + 32$\n$y=-32x+\frac{1}{2}$

Answer

Answer:

C. $y =-\frac{1}{2}x + 32$

Explanation:

Step1: Identify initial amount

Initial juice is 32 cups.

Step2: Determine amount given per student

Each student gets $\frac{1}{2}$ cup. So for $x$ students, amount given is $\frac{1}{2}x$ cups.

Step3: Find remaining amount

Remaining juice $y$ = Initial amount - Amount given. So $y=32-\frac{1}{2}x$, which can be rewritten as $y =-\frac{1}{2}x + 32$.