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) (expand)
2x+8= 4x -8
4x-2x= 8+8 (bring constant to 1 side, x term to the other)
2x= 16 (simplify)
x= 8 (÷2 on both sides)
Beth's present age
= x +2
= 8 +2
= 10 years old
Jimmy's current age
= x
= 8 years old
This question is solved using a system of equations.
I am going to say that:
Doing this, we get that: Beth's present age is 10, and Jimmy's is 8.
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Beth is 2 years older than Jimmy
This means that:
[tex]x = 2 + y[/tex]
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In 3 years the sum of their ages will be twice as much as the sum of their ages 3 years ago.
In 3 years: Beth's age will be x + 3, Jimmy's y + 3.
3 years ago: Beth's x - 3, Jimmy's y - 3.
Thus:
[tex]x + 3 + y + 3 = 2(x - 3 + y - 3)[/tex]
[tex]x + y + 6 = 2(x + y - 6)[/tex]
[tex]x + y + 6 = 2x + 2y - 12[/tex]
[tex]x + y = 18[/tex]
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Since [tex]x = 2 + y[/tex], we solve for Jimmy:
[tex]2 + y + y = 18[/tex]
[tex]2y = 16[/tex]
[tex]y = \frac{16}{2} = 8[/tex]
Beth:
[tex]x = 2 + y = 2 + 8 = 10[/tex]
Beth's present age is 10, and Jimmy's is 8.
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