Question

kira is trying to drink more water and juice each day. the difference in the amount of water in a jug and the amount of juice in the bottle she is drinking from is 192 ounces. she has consumed a total of 42 ounces, which is \\(\frac{3}{32}\\) of the bottle of juice and \\(\frac{9}{84}\\) of the jug of water. which system of equations can be used to determine the total number of ounces in the jug of water, \\(x\\), and the total number of ounces in the bottle of juice, \\(y\\)?\
\\(\circ\\) \\(x - y = 192\\) and \\(\frac{9}{84}x + \frac{3}{32}y = 42\\)\
\\(\circ\\) \\(x - y = 192\\) and \\(\frac{3}{32}x + \frac{9}{84}y = 42\\)\
\\(\circ\\) \\(x + y = 192\\) and \\(\frac{9}{84}x + \frac{3}{32}y = 42\\)\
\\(\circ\\) \\(x + y = 192\\) and \\(\frac{3}{32}x + \frac{9}{84}y = 42\\)

Explanation:

Step1: Set up total difference equation

The difference between water ($x$) and juice ($y$) is 192 ounces:
$x - y = 192$

Step2: Set up consumed amount equation

She drank $\frac{3}{32}$ of juice ($y$) and $\frac{9}{64}$ of water ($x$), totaling 42 ounces:
$\frac{9}{64}x + \frac{3}{32}y = 42$

Answer:

A. $x-y=192$ and $\frac{9}{64}x+\frac{3}{32}y=42$