To find the total number of people at the gym after fourteen more juniors joined, we calculate the original number of adults and juniors using the given ratios, solve for x, and then add the new juniors.
The total number of people is 105.
The question concerns the calculation of the number of people in a gym based on the given ratios of adult to junior members before and after fourteen more juniors joined.
Originally, the ratio of adults to juniors was 7:6. After fourteen more juniors joined, the ratio became 7:8.
Let the original number of adults be 7x and the original number of juniors be 6x.
With the addition of fourteen juniors, the number of juniors became 6x+14.
The new ratio can be expressed as 7x / (6x + 14) = 7/8.
By cross-multiplication, we get:
8(7x) = 7(6x + 14), which simplifies to:
56x = 42x + 98, and further to:
14x = 98, which gives us:
x = 7.
Thus, the original number of adults was 7x = 49 and the original number of juniors was 6x = 42.
After the addition of fourteen juniors, there were 42 + 14 = 56 juniors.
Therefore, the total number of people at the gym after fourteen more juniors joined is 49 adults + 56 juniors = 105.