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)
A) Fill out the table below

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

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

Answer 1

Let's address each part of your question step by step.

### A) Fill out the table

The total amount of food is 360 pounds, and they eat 12 pounds per day. The relationship between the number of days \( x \) and the amount of food left \( y \) can be described by the equation:

\[
y = 360 - 12x
\]

Now we can fill out the table for \( x = 0, 5, 10, 15 \):

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

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

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

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

So the completed table will look like this:

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

### B) Write the equation in slope-intercept form

The equation we've derived is already in slope-intercept form, \( y = mx + b \), where:
- \( m = -12 \) (the slope, representing the rate of food consumption per day),
- \( b = 360 \) (the y-intercept, representing the starting amount of food).

Thus, the equation in slope-intercept form is:

\[
y = -12x + 360
\]

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

To find out when the hikers will run out of food, we need to set \( y = 0 \) in the equation and solve for \( x \):

\[
0 = 360 - 12x
\]

Rearranging the equation:

\[
12x = 360
\]

Dividing both sides by 12:

\[
x = 30
\]

So the hikers will run out of food in 30 days.

**Summary:**
- **Table:** Completed above.
- **Equation:** \( y = -12x + 360 \)
- **Days until food runs out:** 30 days.