Eighty people are separated into 2 groups. The first group is 8 less than 3 times as large as the second. Find the number of people in each group.
smaller group --- x
larger group ---- 3x-8
x + 3x-8 = 80
4x = 88
x = 22
smaller group has 22
larger has 58
To find the number of people in each group, let's first assign variables to the unknown quantities:
Let x be the number of people in the second group.
Then the number of people in the first group is 3x - 8 (since it is 8 less than 3 times the size of the second group).
We know that the total number of people is 80, so we can write the equation:
x + (3x - 8) = 80
Simplifying the equation:
4x - 8 = 80
4x = 88
x = 22
Thus, there are 22 people in the second group.
To find the number of people in the first group, substitute the value of x back into the equation:
3x - 8 = 3(22) - 8 = 66 - 8 = 58
Therefore, there are 22 people in the second group and 58 people in the first group.