Answer:
[tex]\Huge \boxed{{9}}[/tex]
Step-by-step explanation:
Let the age of Darrell be x.
Let the age of Bryce be y.
x = y + 8
xy = 153
Substitute x = y + 8 in the second equation.
(y+8)y = 153
Solve for y.
y² + 8y = 153
Subtract 153 from both sides.
y² + 8y - 153 = 0
Factor left side.
(y-9)(y+17) = 0
Set factors equal to 0.
y - 9 = 0, y = 9
y + 17 = 0, y = -17
The value of y has to be positive, so y = 9.
Substitute y = 9 in the first equation.
x = 9 + 8
x = 17
Darrell is 17 years old.
Bryce is 9 years old.
