7. A group consists of 10 men and 1 woman - OCR - GCSE Maths - Question 10 - 2017 - Paper 2

To determine the age the woman must be in order to maintain the average age after the additional men join, we need to set up the equation based on the new total:

The new total age becomes $T_m + A_w + T_{new}$, where $T_{new}$ is the total age of the 8 new men. The number of people is now 19, so:

$\text{New Average} = \frac{T_m + A_w + T_{new}}{19}$

Setting this new average equal to the previous average gives:

$\frac{T_m + A_w + T_{new}}{19} = \frac{T_m + A_w}{11}$

From here, we can solve for $A_w$ to find the age the woman must be.