Answer: Berma is 5 years old
Rinna is 38 years old
Erwin is 37 years old
Step-by-step explanation:
Let x represent Berma's age
Let y represent Rinna's age
Let z represent Erwin's age
Since the sum of their ages is 80,
x + y + z = 80 - - - - - - -1
Two years from now, Rinna’s age will be 13 less than the sum of Erwin’s age and twice Berma’s age. This means that
y +2 = [ (z+2) + 2(x+2) ] - 13
y +2 = z + 2 + 2x + 4 - 13
2x - y + z = 13 + 2 - 4 -2
2x - y + z = 9 - - - - - - -2
Three years ago, 15 times Berma’s age was 5 less than the age of Rinna. It means that
15(x - 3) = (y - 3) - 5
15x - 45 = y - 3 - 5
15x - y = - 8 + 45
15x - y = 37 - - - - - - - -3
From equation 3, y = 15x - 37
Substituting y = 15x - 37 into equation 1 and equation 2, it becomes
x + 15x - 37 + z = 80
16x + z = 80 + 37 = 117 - - - - - - 4
2x - 15x + 37 + z = 9
-13x + 2 = -28 - - - - - - - - -5
subtracting equation 5 from equation 4,
29x = 145
x = 145/29 = 5
y = 15x - 37
y = 15×5 -37
y = 38
Substituting x= 5 and y = 38 into equation 1, it becomes
5 + 38 + z = 80
z = 80 - 43
z = 37
