Question: c. In this situation, what does the solution to the system mean? 20c + 10m = 495 20c + 10(178.50 -…

c. In this situation, what does the solution to the system mean? 20c + 10m = 495 20c + 10(178.50 - 9c) = 495 20c + 1785 - 90c = 495 20c - 90c + 1785 = 495 - 60c + 1785 = 495

Solution

Step 1: \[ 20c + 10m = 495 \] Step 2: \[ 20c + 10(175.50 - 9c) = 495 \] Step 3: \[ 20c + 1755 - 90c = 495 \] Step 4: \[ 20c - 90c + 1755 = 495 \] Step 5: \[ -60c + 1755 = 495 \] Step 6: \[ -60c = 495 - 1755 \] Step 7: \[ -60c = -1260 \] Step 8: \[ c = \frac{-1260}{-60} = 21 \] Step 9: \[ m = 175.50 - 9c \] Step 10: \[ m = 175.50 - 9(21) = 175.50 - 189 = -13.50 \] The solution to the system is \( c = 21 \) and \( m = -13.50 \). This means that in the given situation, the value of \( c \) is 21, and \( m \) is \(-13.50\). However, a negative value for \( m \) may indicate that there is no feasible solution within the context of the problem.