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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)
10 of 1010 of 10 Items

Question
Directions:

Answer the questions below.
You will be able to check your answers by clicking on "Check Answers" at the bottom.
You can make corrections before submitting this Sample Work.
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 break down the questions step by step.

1) Fill out the table

The hikers begin with 360 pounds of food and consume 12 pounds per day. The relationship between the number of days (x) and the amount of food left (y) can be expressed as:

\[ y = 360 - 12x \]

Now, we can fill out the table by substituting the values of x into the equation to find y.

• 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, the table should look like this:

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

2) Write the equation in slope-intercept form

The equation we derived from the situation is:

\[ y = 360 - 12x \]

This is in slope-intercept form \( y = mx + b \), where \( m = -12 \) (the slope) and \( b = 360 \) (the y-intercept).

3) 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:

\[ 0 = 360 - 12x \]

Solving for \( x \):

1. Add \( 12x \) to both sides: \[ 12x = 360 \]

2. Now divide by 12: \[ x = \frac{360}{12} = 30 \]

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

Summary of Answers

1. Table: | x | y | |----|-----| | 0 | 360 | | 5 | 300 | | 10 | 240 | | 15 | 180 |

2. Equation: \( y = 360 - 12x \)

3. Days to run out of food: 30 days.