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

Explanation:

Step1: Identify initial amount

The teacher starts with 32 - cup of juice.

Step2: Determine amount given per student

Each student is given $\frac{1}{2}$ cup of juice. After $x$ students are served, the total amount of juice given out is $\frac{1}{2}x$ cups.

Step3: Find remaining - juice formula

The remaining amount of juice $y$ is the initial amount minus the amount given out. So $y = 32-\frac{1}{2}x$, which can be rewritten as $y=-\frac{1}{2}x + 32$.

Answer:

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