Answer:
Beth: 10 years old
Jimmy: 8 years old
Step-by-step explanation:
Let Jimmy's present age be x years old.
Since Beth is 2 years older than Jimmy,
Beth's age= (x+2) years old
sum of their ages
= x+x+2
= 2x+2
In 3 years,
Jimmy's age= x+3
Beth's age
= x+2+3
= x+5
Sum if their ages
= x+3 +x+5
= 2x +8
3 years ago,
Jimmy's age= x-3
Beth's age= x+2-3= x-1
sum of ages
=x-3+x-1
= 2x-4
Since in 3 years the sum of their ages will be twice as much as that 3 years ago,
2x+8= 2(2x-4)
2x+8= 2(2x) +2(-4) <em>(expand)</em>
2x+8= 4x -8
4x-2x= 8+8 (<em>bring constant to 1 side, x term to the other</em>)
2x= 16 <em>(simplify)</em>
x= 8 <em>(÷2 on both sides)</em>
Beth's present age
= x +2
= 8 +2
= 10 years old
Jimmy's current age
= x
= 8 years old