Question

A group of hikers begin an expedition with 360 pounds of food.

They plan to eat a total of 12 pounds of food per day.

Let x represent the number of days and y represent the amount of food they have left.

(1 point)
1) Fill out the table below

x y
0
5
10
15
2) Write the equation in slope-intercept form of this situation

3) In how many days will the hikers run out of food?

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Answer 1

Let's tackle the problem step by step.

### 1) Fill out the table below

To find the amount of food left (y) after a certain number of days (x), we can use the relation:

\[
y = 360 - 12x
\]

Now we can fill in the table:

- For **x = 0** (starting point):
\[
y = 360 - 12(0) = 360
\]

- For **x = 5**:
\[
y = 360 - 12(5) = 360 - 60 = 300
\]

- For **x = 10**:
\[
y = 360 - 12(10) = 360 - 120 = 240
\]

- For **x = 15**:
\[
y = 360 - 12(15) = 360 - 180 = 180
\]

So the table is:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
0 & 360 \\
5 & 300 \\
10 & 240 \\
15 & 180 \\
\hline
\end{array}
\]

### 2) Write the equation in slope-intercept form of this situation

The equation relating \(x\) (days) to \(y\) (amount of food left) is:

\[
y = 360 - 12x
\]

This equation is already in slope-intercept form \(y = mx + b\), where:
- \(m = -12\) (the slope, indicating the amount of food consumed per day)
- \(b = 360\) (the y-intercept, indicating the initial amount of food)

### 3) In how many days will the hikers run out of food?

The hikers will run out of food when \(y = 0\):

\[
0 = 360 - 12x
\]

To solve for \(x\):

\[
12x = 360
\]
\[
x = \frac{360}{12} = 30
\]

The hikers will run out of food in **30 days**.