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?

Answer 1

Let’s tackle the questions one by one.

### 1) Fill out the table below

We start with 360 pounds of food and the hikers eat 12 pounds per day. We can calculate the amount of food left (y) after x days using the formula:

\[
y = 360 - 12x
\]

Now we will fill in the table for the given values of x.

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

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

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

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

Now, we can summarize the table:

| x | y |
|-----|-----|
| 0 | 360 |
| 5 | 300 |
| 10 | 240 |
| 15 | 180 |

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

The equation we derived earlier can be expressed in slope-intercept form \(y = mx + b\), where:
- \(m\) is the slope (the rate of food consumption),
- \(b\) is the y-intercept (the initial amount of food).

From our formula \(y = 360 - 12x\):

- The slope \(m = -12\) (meaning they consume 12 pounds per day),
- The y-intercept \(b = 360\) (the initial quantity of food).

Thus, the equation in slope-intercept form is:

\[
y = -12x + 360
\]

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

The hikers will run out of food when \(y = 0\). We can set the equation to zero and solve for \(x\):

\[
0 = 360 - 12x
\]

Rearranging this gives:

\[
12x = 360
\]

Now, dividing both sides by 12, we find:

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

Therefore, the hikers will run out of food in **30 days**.

To summarize:
1. The table is filled out and presented above.
2. The equation is \(y = -12x + 360\).
3. The hikers will run out of food in **30 days**.