Gloria is 20 years older than Reggie.Five years ago she was five times as old as he was. How old is each now?
To solve this problem, we can set up a system of equations and solve them simultaneously. Let's assign variables to Gloria's and Reggie's ages.
Let's say:
- Gloria's current age is G.
- Reggie's current age is R.
According to the given information, Gloria is 20 years older than Reggie. This can be represented as an equation:
G = R + 20 (Equation 1)
And five years ago, Gloria was five times as old as Reggie. This can be represented as another equation:
G - 5 = 5(R - 5) (Equation 2)
Now we have a system of two equations:
1. G = R + 20
2. G - 5 = 5(R - 5)
To solve this system, we can use substitution or elimination method. Let's use substitution:
From Equation 1, we know that G = R + 20. We can substitute this value of G into Equation 2:
(R + 20) - 5 = 5(R - 5)
Simplifying this equation:
R + 15 = 5R - 25
Rearranging the terms:
4R = 40
Dividing both sides by 4:
R = 10
Now we know Reggie's current age is 10. We can substitute this value back into Equation 1 to find Gloria's age:
G = 10 + 20
G = 30
Therefore, Reggie is currently 10 years old, and Gloria is currently 30 years old.
G = R + 20
G - 5 = 5 (R - 5)
substituting ... R + 15 = 5 R - 25