If the owner of a small restaurant bought 75 kilograms of rice and uses 4.5 kilograms each week, what is the function r that represents the remaining amount of rice in kilograms as a function of the number of weeks since the purchase?

Mathematics Questions

If the owner of a small restaurant bought 75 kilograms of rice and uses 4.5 kilograms each week, what is the function r that represents the remaining amount of rice in kilograms as a function of the number of weeks since the purchase?

Short Answer

To calculate the remaining rice after a certain number of weeks, start with the total amount of rice (75 kg) and the weekly consumption rate (4.5 kg). The equation to determine the remaining rice after w weeks is r = 75 – 4.5w, allowing you to see how the rice decreases over time.

Step-by-Step Solution

Step 1: Define Initial Variables

Begin by establishing your initial conditions in the problem. The total amount of rice available is 75 kg. You also need to identify the rate at which rice is consumed, which is 4.5 kg per week. With these figures, you set up two key variables for your calculations:

Total Amount of Rice (T) = 75 kg
Rice Used Per Week (U) = 4.5 kg

Step 2: Set Up the Equation

Now, formulate the equation to represent the remaining rice after a certain number of weeks. Let w denote the number of weeks that have passed. The equation can be structured as:

Remaining Rice (r) = Total Rice (T) – (Rice Used Per Week (U) √ó Number of Weeks (w))

So your equation becomes: r = T – U √ó w

Step 3: Compute the Remaining Rice

Insert the known values into your equation to find the remaining rice after w weeks. Substitute the values of T and U into the equation:

Your final equation for remaining rice is:

r = 75 – 4.5w

This equation shows how the amount of rice diminishes as more weeks progress. You can simply plug different values of w to see how much rice remains after each week.

If the owner of a small…