Question

im mou 5: rice
the owner of a small restaurant is out of rice, so they buy 75 kilograms of rice. each week, the restaurant uses 4.5 kilograms of rice.
function r gives the remaining amount of rice, in kilograms, as a function of the number of weeks, w, since the restaurant owner bought the rice.
part d: solve the equation r(w) = 30, and explain what the solution means in this situation.
when i solved the equation r(w)=30 i got 12.7≈30

Explanation:

Step1: Define the function

The initial amount of rice is 75 kg, and each week 4.5 kg is used. So the function \( r(w) = 75 - 4.5w \), where \( w \) is the number of weeks.

Step2: Solve \( r(w)=30 \)

Set \( 75 - 4.5w = 30 \). Subtract 75 from both sides: \( -4.5w = 30 - 75 = -45 \). Then divide both sides by -4.5: \( w=\frac{-45}{-4.5}=10 \).

Step3: Interpret the solution

The solution \( w = 10 \) means that 10 weeks after buying the 75 kilograms of rice, there will be 30 kilograms of rice remaining.

Answer:

The solution to \( r(w)=30 \) is \( w = 10 \), meaning 10 weeks after purchasing the rice, 30 kilograms remain.