Question

For the past \( m \) days, the average daily production at a company was 100 units per day.
If today’s production of 180 units changes the average to 110 units per day, what is the value of \( m \)?

• A. 18
• B. 10
• C. 7
• D. 5

Hint:

To find the number of days when the average changes after a new addition, set up an equation for the new average and solve for \( m \).

Answer 1

The Correct Option is C

Let the total production for the past \( m \) days be \( 100m \) units. After today's production of 180 units, the total production becomes \( 100m + 180 \). The average production for \( m+1 \) days is given as 110 units. Therefore, we can set up the equation for the average: \[ \frac{100m + 180}{m+1} = 110. \] Multiplying both sides by \( m+1 \) to eliminate the denominator: \[ 100m + 180 = 110(m + 1). \] Expanding the right side: \[ 100m + 180 = 110m + 110. \] Now, subtract \( 100m \) and \( 110 \) from both sides: \[ 180 - 110 = 110m - 100m. \] Simplifying: \[ 70 = 10m. \] Solving for \( m \): \[ m = \frac{70}{10} = 7. \] Thus, the value of \( m \) is 7.