Final answer:
The average age of the two new students who joined the group is 20 years, which raised the average age of the group to 15 years after they joined.
Step-by-step explanation:
The question asks us to find the average age of two new students who joined a group, raising the average age of the now 12-person group by 1 year. To solve this, we start by figuring out the total age of the initial 10 students. With an average age of 14 years, the total age for the original group is 10 students × 14 years/student = 140 years. When the two new students join, the average age increases to 15 years for the 12 students. The new total age is 12 students × 15 years/student = 180 years.
The combined age of the two new students must account for the difference between the new total age and the original total age. So, the combined age of the two new students is 180 years - 140 years = 40 years. To find the average age of the two students, we divide the combined age by the number of new students: 40 years ÷ 2 students = 20 years per student. Therefore, the average age of the two new students is 20 years.