Ask a New Question
Menu

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? Skip to navigation

1 answer

  1. To fill out the table, we need to calculate the amount of food left (y) for different values of days (x).

  • Day 0 (x = 0): Food left = Total food - (Food consumed in 0 days)
    \(y = 360 - 12(0) = 360\)

  • Day 5 (x = 5): Food left = Total food - (Food consumed in 5 days)
    \(y = 360 - 12(5) = 360 - 60 = 300\)

  • Day 10 (x = 10): Food left = Total food - (Food consumed in 10 days)
    \(y = 360 - 12(10) = 360 - 120 = 240\)

  • Day 15 (x = 15): Food left = Total food - (Food consumed in 15 days)
    \(y = 360 - 12(15) = 360 - 180 = 180\)

So the table is:

| x (days) | y (food left in pounds) | |----------|--------------------------| | 0 | 360 | | 5 | 300 | | 10 | 240 | | 15 | 180 |

  1. The equation in slope-intercept form can be derived from the relationship between the days and the food left. The slopes represent the rate of food consumption, and the intercept represents the initial amount of food.

The linear equation can be expressed as: \[ y = mx + b \] where \(m\) is the slope (rate of food consumption) and \(b\) is the y-intercept (initial amount of food).

Here, the slope \(m = -12\) (since they are consuming 12 pounds per day) and \(b = 360\).

Thus, the equation is: \[ y = -12x + 360 \]

  1. To find out in how many days the hikers will run out of food, set \(y = 0\) and solve for \(x\):

\[ 0 = -12x + 360 \] \[ 12x = 360 \] \[ x = \frac{360}{12} = 30 \]

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