Question

a glass of milk is poured from a fresh 1-gallon jug. the following data table shows how much milk is left in the jug after a specific number of glasses are poured. (hint: a full 1-gallon jug has 128 ounces of milk in it.)

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$$\begin{tabular}{|c|c|} \\hline glasses (\\#) & milk remaining (ounces) \\\\ \\hline 1 & 118 \\\\ 2 & 108 \\\\ 4 & 88 \\\\ 6 & 68 \\\\ \\hline \\end{tabular}$$

how much milk is left in the jug after 8 large glasses are poured?

Explanation:

Identify the initial state and given data

The initial volume of milk in a full 1-gallon jug is \(128\) ounces. Let \(x\) represent the number of glasses poured, and \(y\) represent the remaining milk in ounces. The given data points are:

• For \(x = 1\), \(y = 118\)
• For \(x = 2\), \(y = 108\)
• For \(x = 4\), \(y = 88\)
• For \(x = 6\), \(y = 68\)

Determine the rate of change

We calculate the change in remaining milk per glass poured:

$$ \text{Rate} = \frac{108 - 118}{2 - 1} = \frac{-10}{1} = -10\text{ ounces per glass} $$

We verify this constant rate with another interval:

$$ \text{Rate} = \frac{68 - 88}{6 - 4} = \frac{-20}{2} = -10\text{ ounces per glass} $$

Each glass holds exactly \(10\) ounces of milk.

Formulate the linear equation

Using the initial value of \(128\) ounces at \(x = 0\), the linear relationship is:

$$ y = 128 - 10x $$

We verify this equation with \(x = 1\):

$$ y = 128 - 10(1) = 118 $$

This matches the table.

Calculate the remaining milk for 8 glasses

We substitute \(x = 8\) into our linear equation:

$$ y = 128 - 10(8) $$

$$ y = 128 - 80 = 48 $$

Thus, \(48\) ounces of milk remain.

Answer:

How much milk is left in the jug after 8 large glasses are poured? <blank>48</blank>