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.

Question

x y
0 ___
5 ____
10 _____
15 _____
Write the equation in slope intercept form of this situation
In how many days will the hikers run out of food

Answer 1

To analyze this situation, we can start with the information provided.

1. The hikers begin with 360 pounds of food.
2. They eat 12 pounds of food per day.

Let \( x \) be the number of days and \( y \) be the amount of food left after \( x \) days.

Given that they start with 360 pounds, the relationship between \( x \) (the number of days) and \( y \) (the amount of food left) can be expressed with the following equation:

\[ y = 360 - 12x \]

This equation is in slope-intercept form \( y = mx + b \) where:

• \( m \) is the slope (which is -12, indicating the food decreases by 12 pounds each day)
• \( b \) is the y-intercept (which is 360, indicating the starting amount of food).

Now, we can fill in the table for the amounts of food left using this equation.

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 is as follows:

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

Next, to find out in how many days the hikers will run out of food, we need to find when \( y = 0 \):

Setting the equation to zero: \[ 0 = 360 - 12x \] Solving for \( x \): \[ 12x = 360 \ x = \frac{360}{12} = 30 \]

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